Aline Bonami, Justin Feuto
We define as a distribution the product of a function (or distribution) h in some Hardy space Hp with a function b in the dual space of Hp. Moreover, we prove that the product bxh may be written as the sum of an integrable function with a distribution that belongs to some Hardy-Orlicz space, or to the same Hardy space Hp, depending on the values of p.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
This paper obtains new characterizations of weighted Hardy spaces and certain weighted $BMO$ type spaces via the boundedness of variation operators associated with approximate identities and their commutators, respectively.
Hardy-Littlewood maximal, generalized Bessel-Riesz and generalized fractional integral operators in generalized Morrey and $BMO_ϕ$ spaces associated with Dunkl operator on the real line
本文研究了与Dunkl算子相关的广义Morrey和$BMO_ϕ$空间中Hardy-Littlewood极大函数、Bessel-Riesz算子和广义分数积分算子的有界性问题。
In this paper, we introduce a new weighted Hardy-Cesàro operator defined by $U_{ψ,s}f(x)=\int\limits_0^1 f(s(t)\cdot x) ψ(t)dt$, which is associated to the parameter curve $s(t,x)=s(t)x$. Under certain conditions on $s(t)$ and on an absolutely homogeneous weight function $ω$, we characterize the weight function $ψ$ such that $U_{ψ,s}$ is bounded on $L^p(ω)$, $BMO(ω)$. The corresponding operator norms are worked out too. These results extend the ones of Jie Xiao \cite{xiao}. We also give a sufficient and a necessary condition on the weight function $ψ$, which ensure the boundedness of the commu…
In this paper, we establish sufficient conditions for a singular integral $T$ to be bounded from certain Hardy spaces $H^p_L$ to Lebesgue spaces $L^p$, $0< p \le 1$, and for the commutator of $T$ and a BMO function to be weak-type bounded on Hardy space $H_L^1$. We then show that our sufficient conditions are applicable to the following cases: (i) $T$ is the Riesz transform or a square function associated with the Laplace-Beltrami operator on a doubling Riemannian manifold, (ii) $T$ is the Riesz transform associated with the magnetic Schrödinger operator on an Euclidean space, and (iii) $T = g…
In this paper, the authors studied the fractional S-transform on BMO and Hardy spaces and generalized the results given in \cite{Singh15h}. In introduction section, the definitions of the S-transform, fractional Fourier transform and fractional S-transform are given. In Section 2 continuity and boundedness results for the fractional S-transform in BMO and Hardy spaces are obtained. Furthermore, in Section 3 the fractional S-transform is studied on the weighted BMO$_κ$ and weighted Hardy spaces associated with a tempered weight function.
This article is devoted to a study of the Hardy space $H^{\log} (\mathbb{R}^d)$ introduced by Bonami, Grellier, and Ky. We present an alternative approach to their result relating the product of a function in the real Hardy space $H^1$ and a function in $BMO$ to distributions that belong to $H^{\log}$ based on dyadic paraproducts. We also point out analogues of classical results of Hardy-Littlewood, Zygmund, and Stein for $H^{\log}$ and related Musielak-Orlicz spaces.
It is well known that if Hardy-Littlewood maximal operator is bounded in space $L^{p(\cdot)}[0;1]$ then $1/p(\cdot)\in BMO^{1/\log}$. On the other hand if $p(\cdot)\in BMO^{1/\log},$ ($1<p_{-}\leq p_{+}<\infty$), then there exists $c>0$ such that Hardy-Littlewood maximal operator is bounded in $L^{p(\cdot)+c}[0;1].$ Also There exists exponent $p(\cdot)\in BMO^{1/\log},$ ($1<p_{-}\leq p_{+}<\infty$) such that Hardy-Littlewood maximal operator is not bounded in $L^{p(\cdot)}[0;1]$. In the present paper we construct exponent $p(\cdot),$ $(1<p_{-}\leq p_{+}<\infty)$, $1/p(\cdot)\in BLO^{1/\log}$ s…
We describe the spaces $H^1(R)$ and BMO$(R)$ in terms of their closely related, simpler dyadic and two-sided counterparts. As a result of these characterizations we establish when a bounded linear operator defined on dyadic or two-sided $H^1(R)$ into a Banach space has a continuous extension to $H^1(R)$ and when a bounded linear operator that maps a Banach space into dyadic or two-sided BMO$(R)$ actually maps continuously into BMO$(R)$.
BMO-Type characterizations and endpoint estimates for commutators of intrinsic square functions on Orlicz-Hardy spaces
本文研究内蕴平方函数交换子，证明其有界性等价于BMO型空间成员资格，并将加权结果推广至Musielak-Orlicz与Orlicz-Hardy空间，给出端点估计。
Fix $λ>0$. Consider the Hardy space $H^1(\mathbb{R}_+,dm_λ)$ in the sense of Coifman and Weiss, where $\mathbb{R_+}:=(0,\infty)$ and $dm_λ:=x^{2λ}dx$ with $dx$ the Lebesgue measure. Also consider the Bessel operators $Δ_λ:=-\frac{d^2}{dx^2}-\frac{2λ}{x} \frac d{dx}$, and $S_λ:=-\frac{d^2}{dx^2}+\frac{λ^2-λ}{x^2}$ on $\mathbb{R_+}$. The Hardy spaces $H^1_{Δ_λ}$ and $H^1_{S_λ}$ associated with $Δ_λ$ and $S_λ$ are defined via the Riesz transforms $R_{Δ_λ}:=\partial_x (Δ_λ)^{-1/2}$ and $R_{S_λ}:= x^λ\partial_x x^{-λ} (S_λ)^{-1/2}$, respectively. It is known that $H^1_{Δ_λ}$ and $H^1(\mathbb{R}_+,d…
The sharp reverse Hardy inequality in BMO for nonincreasing functions
本文针对正实数集上的Hardy算子，证明了非增局部可积函数的反向Hardy不等式中Korenovskii提出的因子e/4可去除，得到最优常数α₀，解决了相关猜想。
UMD-valued square functions associated with Bessel operators in Hardy and BMO spaces
本文研究 Bessel 背景下 Banach 取值 Hardy 和 BMO 空间，利用分数阶导数定义平方函数，证明了 UMD 空间中涉及 $γ$-radonifying 算子的等价范数，并基于 g-函数的有界性刻画了 UMD Banach 空间。
Let $Γ$ be a graph with the doubling property for the volume of balls and $P$ a reversible random walk on $Γ$. We introduce $H^1$ Hardy spaces of functions and $1$-forms adapted to $P$ and prove various characterizations of these spaces. We also characterize the dual space of $H^1$ as a $BMO$-type space adapted to $P$. As an application, we establish $H^1$-$H^1$ and $H^1$-$L^1$ boundedness of the Riesz transform.
$γ$-radonifying operators and UMD-valued Littlewood-Paley-Stein functions in the Hermite setting on BMO and Hardy spaces
本文研究了 Hermite 算子下取值于 UMD Banach 空间的 Littlewood-Paley-Stein 函数，证明了 Hermite 平方函数在 BMO 和 Hardy 空间上的有界性，并给出了这些空间的等价范数及 UMD Banach 空间的新刻画。
In this paper we establish the product Hardy spaces associated with the Bessel Schrödinger operator introduced by Muckenhoupt and Stein, and provide equivalent characterizations in terms of the Bessel Riesz transforms, non-tangential and radial maximal functions, and Littlewood--Paley theory, which are consistent with the classical product Hardy space theory developed by Chang and Fefferman. Moreover, in this specific setting, we also provide another characterization via the Telyakovskií transform, which further implies that the product Hardy space associated with this Bessel Schrödinger opera…
Hardy and BMO spaces on Weyl chambers
本文在由同态赋予边界符号的框架下，定义并研究了正Weyl腔上的Hardy与BMO空间，针对正交根系建立了原子分解并讨论了对偶问题。
In this note, we aim to describe sharp constants for the composition operator with a bi-Lipschitz measure-preserving map in several functional spaces (BMO, Hardy space, Carleson measures, ...). It is interesting to see how the measure preserving property allows us to improve these constants. Moreover, we will prove the optimality of our results for the BMO space and describe improved estimates for solutions of transport PDEs.
Let $M$ be the Hardy-Littlewood maximal function and $b$ be a locally integrable function. Denote by $M_b$ and $[b,M]$ the maximal commutator and the (nonlinear) commutator of $M$ with $b$. In this paper, the author consider the boundedness of $M_b$ and $[b,M]$ on Lebesgue spaces and Morrey spaces when $b$ belongs to the Lipschitz space, by which some new characterizations of the Lipschitz spaces are given.
Let $Ω$ be a strongly Lipschitz domain of $\reel^n$. Consider an elliptic second order divergence operator $L$ (including a boundary condition on $\partialΩ$) and define a Hardy space by imposing the non-tangential maximal function of the extension of a function $f$ via the Poisson semigroup for $L$ to be in$L^1$. Under suitable assumptions on $L$, we identify this maximal Hardy space with atomic Hardy spaces, namely with $H^1(\reel^n)$ if $Ω=\reel^n$, $H^{1}_{r}(Ω)$ under the Dirichlet boundary condition, and $H^{1}_{z}(Ω)$ under the Neumann boundary condition. In particular, we obtain a new …
Let S be the semidirect product of R^d and R^+ endowed with the Riemannian symmetric space metric and the right Haar measure: this is a Lie group of exponential growth. In this paper we define an Hardy space H^1 and a BMO space in this context. We prove that the functions in BMO satisfy the John-Nirenberg inequality and that BMO may be identified with the dual space of H^1. We then prove that singular integral operators which satisfy a suitable integral Hormander condition are bounded from H^1 to L^1 and from L^{\infty} to BMO. We also study the real interpolation between H^1, BMO and the L^p …
We obtain Fourier inequalities in the weighted $L_p$ spaces for any $1<p<\infty$ involving the Hardy-Cesàro and Hardy-Bellman operators. We extend these results to product Hardy spaces for $p\le 1$. Moreover, boundedness of the Hardy-Cesàro and Hardy-Bellman operators in various spaces (Lebesgue, Hardy, BMO) is discussed. One of our main tools is an appropriate version of the Hardy-Littlewood-Paley inequality $ \|\widehat{f}\|_{L_{p',q}} \lesssim \left\|f\right\|_{L_{p,q}}$.
This paper provides a deeper study of the Hardy and $\rm BMO$ spaces associated to the Neumann Laplacian $Δ_N$. For the Hardy space $H^1_{Δ_N}(\mathbb{R}^n)$ (which is a proper subspace of the classical Hardy space $H^1(\mathbb{R}^n)$) we demonstrate that the space has equivalent norms in terms of Riesz transforms, maximal functions, atomic decompositions, and weak factorizations. While for the space ${\rm BMO}_{Δ_N}(\mathbb{R}^n)$ (which contains the classical $\rm BMO(\mathbb{R}^n)$) we prove that it can be characterized in terms of the action of the Riesz transforms associated to the Neuman…
Let $L$ be a linear operator on $L^2(\mathbb R^n)$ generating an analytic semigroup $\{e^{-tL}\}_{t\ge0}$ with kernels having pointwise upper bounds and $p(\cdot):\ \mathbb R^n\to(0,1]$ be a variable exponent function satisfying the globally log-Hölder continuous condition. In this article, the authors introduce the variable exponent Hardy space associated with the operator $L$, denoted by $H_L^{p(\cdot)}(\mathbb R^n)$, and the BMO-type space ${\mathrm{BMO}}_{p(\cdot),L}(\mathbb R^n)$. By means of tent spaces with variable exponents, the authors then establish the molecular characterization of…
This paper provides a constructive proof of the weak factorizations of the classical Hardy space $H^1(\mathbb{R}^n)$ in terms of multilinear Riesz transforms. As a direct application, we obtain a new proof of the characterization of ${\rm BMO}(\mathbb{R}^n)$ (the dual of $H^1(\mathbb{R}^n)$) via commutators of the multilinear Riesz transforms.
A general class of weighted multilinear Hardy-Cesàro operators that acts on the product of Lebesgue spaces and central Morrey spaces. Their sharp bounds are also obtained. In addition, we obtain sufficient and necessary conditions on weight functions so that the commutators of these weighted multilinear Hardy-Cesàro operators (with symbols in central BMO space) are bounded on the product of central Morrey spaces. These results extends known results on multilinear Hardy operators.
Hardy spaces, Campanato spaces and higher order Riesz transforms associated with Bessel operators
本文针对多元Bessel算子$Δ_ν$，建立了相关Hardy空间与BMO型空间理论，证明其高阶Riesz变换为Calderón-Zygmund算子且在上述空间上有界，推进了Bessel算子框架下的调和分析研究。
We prove a sufficient condition for frame-type wavelet series in $L^p$, the Hardy space $H^1$, and BMO. For example, functions in these spaces are shown to have expansions in terms of the Mexican hat wavelet, thus giving a strong answer to an old question of Meyer. Bijectivity of the wavelet frame operator acting on Hardy space is established with the help of new frequency-domain estimates on the Calderón-Zygmund constants of the frame kernel.
Quantitative BMO-BLO Estimates for the Hardy-Littlewood Maximal Function
本文研究了Hardy-Littlewood极大函数在BMO-BLO空间中的量化估计，扩展了经典结果并给出了A_∞类的新刻画。
Characterizations of a class of Musielak--Orlicz BMO spaces via commutators of Riesz potential operators
本文研究了通过Riesz势算子的交换子将Musielak-Orlicz Hardy空间映射到Musielak-Orlicz空间的条件，提出了新的BMO子空间定义并验证了其有界性。
We give a div-curl type lemma for the wedge product of closed differential forms on R^n when they have coefficients respectively in a Hardy space and L^infinity or BMO. In this last case, the wedge product belongs to an appropriate Hardy-Orlicz space.
In this paper, we pursue the study of harmonic functions on the real hyperbolic ball started by the second named author. Our focus here is on the theory of Hardy, Hardy-Sobolev and Lipschitz spaces of these functions. We prove here that these spaces admit Fefferman-Stein like characterizations in terms of maximal and square functionals. We further prove that the hyperbolic harmonic extension of Lipschitz functions on the boundary extend into Lipschitz functions on the whole ball.
This paper is concerned with the problem of decomposing a higher order Lipschitz function on a closed Jordan curve $Γ$ into a sum of two polyanalytic functions in each open domain defined by $Γ$. Our basic tools are the Hardy projections related to a singular integral operator arising in polyanalytic function theory, which, as it is proved here, represents an involution operator on the higher order Lipschitz classes. Our result generalizes the classical Hardy decomposition of Holder continuous functions on the boundary of a domain.
We study boundedness properties of a class of multiparameter paraproducts on the dual space of the dyadic Hardy space H_d^1(T^N), the dyadic product BMO space BMO_d(T^N). For this, we introduce a notion of logarithmic mean oscillation on the polydisc. We also obtain a result on the boundedness of iterated commutators on BMO([0,1]^2).
Hardy spaces and Campanato spaces associated with Laguerre expansions and higher order Riesz transforms
本文针对拉盖尔微分算子\mathcal{L}_ν，建立了全范围\\\\(p \in (0,1]\\\\)的相关哈代空间理论，证明了对应BMO型空间是其对偶空间，并验证了高阶里斯变换在勒贝格空间等上的有界性。
Let $ϕ: \mathbb{R}^n\times[0,\fz)\rightarrow[0,\fz)$ be a function such that $ϕ(x,\cdot)$ is an Orlicz function and $ϕ(\cdot,t)\in A^{\mathop\mathrm{loc}}_{\infty}(\mathbb{R}^n)$ (the class of local weights introduced by V. S. Rychkov). In this paper, the authors introduce a local Hardy space $h_ϕ(\mathbb{R}^n)$ of Musielak-Orlicz type by the local grand maximal function, and a local $\mathop\mathrm{BMO}$-type space $\mathop\mathrm{bmo}_ϕ(\mathbb{R}^n)$ which is further proved to be the dual space of $h_ϕ(\mathbb{R}^n)$. As an application, the authors prove that the class of pointwise multipli…
Let $0<α<n$ and $M_α$ be the fractional maximal function. The nonlinear commutator of $M_α$ and a locally integrable function $b$ is given by $[b,M_α](f)=bM_α(f)-M_α(bf)$. In this paper, we mainly give some necessary and sufficient conditions for the boundedness of $[b,M_α]$ on variable Lebesgue spaces when $b$ belongs to Lipschitz or $BMO(\rn)$ spaces, by which some new characterizations for certain subclasses of Lipschitz and $BMO(\rn)$ spaces are obtained.
Dunkl--BMO functions representable in terms of generalized balayage of Carleson measures and an application
本文刻画了Dunkl--BMO空间中紧支撑函数为有界函数与Carleson测度广义扫集之和，并由此通过主值积分建立了Dunkl框架下Hardy空间的新刻画，且结论推广至热半群。
Lusin Area Function and Molecular Characterizations of Musielak-Orlicz Hardy Spaces and Their ApplicationsLet $φ: \mathbb R^n\times [0,\infty)\to[0,\infty)$ be a growth function such that $φ(x,\cdot)$ is nondecreasing, $φ(x,0)=0$, $φ(x,t)>0$ when $t>0$, $\lim_{t\to\infty}φ(x,t)=\infty$, and $φ(\cdot,t)$ is a Muckenhoupt $A_\infty(\mathbb{R}^n)$ weight uniformly in $t$. In this paper, the authors establish the Lusin area function and the molecular characterizations of the Musielak-Orlicz Hardy space $H_φ(\mathbb{R}^n)$ introduced by Luong Dang Ky via the grand maximal function. As an applicatio…
Let ${\mathcal X}$ be a metric space with doubling measure, $L$ a nonnegative self-adjoint operator in $L^2({\mathcal X})$ satisfying the Davies-Gaffney estimate, $ω$ a concave function on $(0,\infty)$ of strictly lower type $p_ω\in (0, 1]$ and $ρ(t)={t^{-1}}/ω^{-1}(t^{-1})$ for all $t\in (0,\infty).$ The authors introduce the Orlicz-Hardy space $H_{ω,L}({\mathcal X})$ via the Lusin area function associated to the heat semigroup, and the BMO-type space ${\mathop\mathrm{BMO}_{ρ,L}(\mathcal X)}$. The authors then establish the duality between $H_{ω,L}({\mathcal X})$ and $\mathrm{BMO}_{ρ,L}({\mat…
Sharp bounds for the multilinear integral operators on Heisenberg group BMO space
本文研究了 Heisenberg 群 BMO 空间上的 m-线性 n-维 Hardy-Littlewood-Pólya 算子与 Hilbert 算子，并证明了这两个算子在该空间中的有界性。
We give a constructive proof of the factorization theorem for the classical Hardy space in terms of fractional integral operator. Moreover, the result is extended to the multilinear case and weighted case. As an application, we obtain the characterization of $BMO$ via the weighted boundedness of commutators of the multilinear fractional integral operator, without individual conditions on the weights class.
We first consider two types of localizations of singular integral operators of convolution type, and show, under mild decay and smoothness conditions on the auxiliary functions, that their boundedness on the local Hardy space $h^1(\mathbb{R}^n)$ is equivalent. We then study the boundedness on $h^1(\mathbb{R}^n)$ of the commutator $[b,T]$ of an inhomogeneous singular integral operator with $b$ in $bmo(\mathbb{R}^n)$, the nonhomogeneous space of functions of bounded mean oscillation. We define local analogues of the atomic space $H^1_b(\mathbb{R}^n)$ introduced by Pérez in the case of the homoge…
Let $0<ρ<n$ and $μ^ρ_Ω$ be the parametric Marcinkiewicz integral. In this paper, by using the atomic decomposition theory of weighted Hardy and weak Hardy spaces, we will obtain the boundedness properties of $μ^ρ_Ω$ on these spaces, under the Lipschitz condition imposed on the kernel $Ω$.
Global Stein Theorem on Hardy spaces
本文研究保证可积函数属于Hardy空间H^1及H^log的关于|f|的最大条件，特别关注无穷远处的条件，推广了紧支撑情形下的L log L充分必要条件。
Under the assumption that the underlying measure is a non-negative Radon measure which only satisfies some growth condition and may not be doubling, we define the product of functions in the regular $BMO$ and the atomic block $\H^{1}$ in the sense of distribution, and show that this product may be split into two parts, one in $L^{1}$ and the other in some Hardy-Orlicz space.
Let $\mathcal{X}$ be a metric space with doubling measure and $L$ a nonnegative self-adjoint operator in $L^2(\mathcal{X})$ satisfying the Davies-Gaffney estimates. Let $φ:\,\mathcal{X}\times[0,\infty)\to[0,\infty)$ be a function such that $φ(x,\cdot)$ is an Orlicz function, $φ(\cdot,t)\in A_{\infty}(\mathcal{X})$ (the class of Muckenhoupt weights) and its uniformly critical lower type index $i(φ)\in(0,1]$. In this paper, the authors introduce a Musielak-Orlicz Hardy space $H_{φ,\,L}(\mathcal{X})$ by the Lusin area function associated with the heat semigroup generated by $L$, and a Musielak-Or…
Let $Φ$ be a concave function on $(0,\infty)$ of strictly lower type $p_Φ\in(0,1]$ and $ω\in A^{\mathop\mathrm{loc}}_{\infty}(\mathbb{R}^n)$. We introduce the weighted local Orlicz-Hardy space $h^Φ_ω(\mathbb{R}^n)$ via the local grand maximal function. Let $ρ(t)\equiv t^{-1}/Φ^{-1}(t^{-1})$ for all $t\in(0,\infty)$. We also introduce the $\mathop\mathrm{BMO}$-type space $\mathop\mathrm{bmo}_{ρ,\,ω}(\mathbb{R}^n)$ and establish the duality between $h^Φ_ω(\mathbb{R}^n)$ and $\mathop\mathrm{bmo}_{ρ,\,ω}(\mathbb{R}^n)$. Several real-varaiable characterizations of $h^Φ_ω(\mathbb{R}^n)$ are presente…
Recovering Product BMO from Schatten Hankel operators
研究证明小Hankel算子属于Schatten类时，其符号属于乘积BMO，扩展了Nehari定理的条件。
In this paper, the author obtain the continuity of a class of linear operators on variable anisotropic Hardy-Lorentz spaces. In addition, the author also obtain that the dual space of variable anisotropic Hardy-Lorentz spaces is the anisotropic BMO-type spaces with variable exponents. This result is still new even when the exponent function $p(\cdot)$ is $p$.
Some characterizations of BMO and Lipschitz spaces in the Schrödinger setting
本文针对薛定谔算子相关的BMO和Lipschitz空间，给出若干新刻画，将已有研究结果推广到权类范围大于经典Muckenhoupt类的加权情形。
We introduce the iterated commutator for the Riesz transforms in the multi-parameter flag setting, and prove the upper bound of this commutator with respect to the symbol $b$ in the flag BMO space. Our methods require the techniques of semigroups, harmonic functions and multi-parameter flag Littlewood-Paley analysis. We also introduce the big commutator in this multi-parameter flag setting and prove the upper bound with symbol $b$ in the flag little-bmo space by establishing the "exponential-logarithmic" bridge between this flag little bmo space and the Muckenhoupt $A_p$ weights with flag stru…
Bounded oscillation operators on BMO spaces
本文研究了BO算子在BMO空间上的有界性，证明了其将L^∞映射到BMO，并在特定条件下保持BMO的自映射性质。
The aim of this article is to give a complete solution to the problem of the bilinear decompositions of the products of some Hardy spaces $H^p(\mathbb{R}^n)$ and their duals in the case when $p<1$ and near to $1$, via wavelets, paraproducts and the theory of bilinear Calderón-Zygmund operators. Precisely, the authors establish the bilinear decompositions of the product spaces $H^p(\mathbb{R}^n)\times\dotΛ_α (\mathbb{R}^n)$ and $H^p(\mathbb{R}^n)\timesΛ_α(\mathbb{R}^n)$, where, for all $p\in(\frac{n}{n+1},\,1)$ and $α:=n(\frac{1}{p}-1)$, $H^p(\mathbb{R}^n)$ denotes the classical real Hardy spac…
Let $dγ(x)\equivπ^{-n/2}e^{-|x|^2}dx$ for all $x\in{\mathbb R}^n$ be the Gauss measure on ${\mathbb R}^n$. In this paper, the authors establish the characterizations of the space BMO$(γ)$ of Mauceri and Meda via commutators of either local fractional integral operators or local fractional maximal operators. To this end, the authors first prove that such a local fractional integral operator of order $β$ is bounded from $L^p(γ)$ to $L^{p/(1-pβ)}(γ)$, or from the Hardy space $H^1(γ)$ of Mauceri and Meda to $L^{1/(1-β)}(γ)$ or from $L^{1/β}(γ)$ to BMO$(γ)$, where $β\in(0, 1)$ and $p\in(1, 1/β)$.
Recently, both the bilinear decompositions $h^1(\mathbb{R}^n)\times \mathrm{\,bmo}(\mathbb{R}^n) \subset L^1 (\mathbb{R}^n)+h_\ast^Φ(\mathbb{R}^n)$ and $h^1(\mathbb{R}^n) \times \mathrm{bmo}(\mathbb{R}^n) \subset L^1 (\mathbb{R}^n) + h^{\log}(\mathbb{R}^n)$ were established. In this article, the authors prove in some sense that the former is sharp, while the latter is not. To this end, the authors first introduce the local Orlicz-slice Hardy space which contains the variant $h_\ast^Φ(\mathbb{R}^n)$ of the local Orlicz Hardy space introduced by A. Bonami and J. Feuto as a special case, and obta…
We study the holomorphic Hardy-Orlicz spaces H^Φ(Ω), where Ωis the unit ball or, more generally, a convex domain of finite type or a strictly pseudoconvex domain in Cn . The function Φis in particular such that H ^1(Ω) \subset H^Φ(Ω) \subset H ^p (Ω) for some p > 0. We develop for them maximal characterizations, atomic and molecular decompositions. We then prove weak factorization theorems involving the space BMOA(Omega). As a consequence, we characterize those Hankel operators which are bounded from H ^Φ(Ω) into H^1 (Ω).
A note on weak factorization of Meyer-type Hardy space via Cauchy integral operator
本文提供了梅耶型Hardy空间H^1_b(R)的弱分解，并通过与柯西积分C_Γ相关的有界性和紧性刻画其对偶空间BMO_b(R)和其预对偶空间VMO_b(R)
We give an extension to certain \textit{RD-space} $\X$, i.e space of homogeneous type in the sense of Coifman and Weiss, which has the reverse doubling property, of the definition and various properties of the product of functions in $\BMO(\X)$ and $\H^{1}(\X)$, and functions in Lipschitz space $Λ_{\frac{1}{p}-1}(\X)$ and $\H^{p}(\X)$ for $p\in(\frac{\n}{\n+θ},1]$, where $\n$ and $θ$ denote respectively the "dimension" and the order of $\X$
Let $Ω$ be a strongly Lipschitz domain of $\mathbb{R}^n$, whose complement in $\mathbb{R}^n$ is unbounded. Let $L$ be a second order divergence form elliptic operator on $L^2 (Ω)$ with the Dirichlet boundary condition, and the heat semigroup generated by $L$ have the Gaussian property $(G_{\mathrm{diam}(Ω)})$ with the regularity of their kernels measured by $μ\in(0,1]$, where $\mathrm{diam}(Ω)$ denotes the diameter of $Ω$. Let $Φ$ be a continuous, strictly increasing, subadditive and positive function on $(0,\infty)$ of upper type 1 and of strictly critical lower type $p_Φ\in(n/(n+μ),1]$. In t…
Let 0<n<d be integers and let H denote the n-dimensional Hausdorff measure restricted to an n-dimensional Lipschitz graph in R^d with slope strictly less than 1. For r>2, we prove that the r-variation and oscillation for Calderón-Zygmund singular integrals with odd kernel are bounded operators in L^p(H) for 1<p finite, from L^1(H) to weak-L^1(H), and from the space of bounded H-measurable functions to BMO(H). Concerning the first endpoint estimate, we actually show that such operators are bounded from the space of finite complex Radon measures in R^d to weak-L^1(H).
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。