Function Theory in Real Hardy Spaces

Different approach to the decomposition theory of $HM^p_{q,{Δ_ν}}$ Hardy-Morrey spaces

The Hardy-Morrey spaces related to Laplace-Bessel differential equations are introduced in terms of maximal functions. The atomic decomposition theory which has the same cancellation properties of the $H^{p}_{Δ_ν}(\mathbb{R}^{n}_{+})$ Hardy spaces is established.

Weighted composition, Volterra and Integral operators on Hardy Zygmund-type spaces

In this paper, we investigate weighted composition, Volterra and Integral operators on second derivative Hardy spaces. Some equivalent conditions for boundedness of the operators will be given using the boundedness on the Hardy spaces. Also we give a criteria for compactness of weighted composition operators.

Conditions for Boundedness into Hardy spaces

We obtain boundedness from a product of Lebesgue or Hardy spaces into Hardy spaces under suitable cancellation conditions for a large class of multilinear operators that includes the Coifman-Meyer class, sums of products of linear Calderon-Zygmund operators and combinations of these two types.

Some results on the Hardy space H1 associated with the Dunkl operators

In the present paper, we investigate in Dunkl analysis, the action of some fundamental operators on the atomic Hardy space H1.

Certain properties of continuous fractional wavelet transform on Hardy space and Morrey space

In this paper we define a new class of continuous fractional wavelet transform (CFrWT) and study its properties in Hardy space and Morrey space. The theory developed generalize and complement some of already existing results.

Weighted Grand Lebesgue Spaces norm estimation for Hardy-Sobolev-Poincare-Wirtinger operators

We extend the classical Hardy-Sobolev-Poincare-Wirtinger inequalities from the ordinary Lebesgue-Riesz spaces into the Grand Lebesgue ones, with exact constants evaluation.

Closed Range Integral Operators on Hardy, BMOA and Besov Spaces

In this paper, we prove three necessary and sufficient conditions for the integral operator Sg to have closed range on Hardy Hp (1<p<\infty), BMOA and Besov Bp (1<p<\infty) spaces.

A characterization of weighted local Hardy spaces

In this paper, we give a characterization of weighted local Hardy spaces $h^1_\wz(\rz)$ associated with local weights by using the truncated Reisz transforms, which generalizes the corresponding result of Bui in \cite{b}.

Approximation numbers of composition operators on the Hardy space of the ball and of the polydisk

We give general estimates for the approximation numbers of composition operators on the Hardy space on the ball $B\_d$ and the polydisk $D^d$ .

Sharp Weight Hardy-Sobolev inequalities for Grand Lebesgue Spaces

We give in this short paper the exact value for norms of two operators of Hardy-Sobolev type acting between two weight Grand Lebesgue Space (GLS) based on the whole multidimensional Euclidean space.

An embedding constant for the Hardy space of Dirichlet series

A new and simple proof of the embedding of the Hardy--Hilbert space of Dirichlet series into a conformally invariant Hardy space of the half-plane is presented, and the optimal constant of the embedding is computed.

Two-Weighted Inequalities for Hardy-Littlewood Maximal Functions and Singular Integrals in $l^{p(\cdot)}$ Spaces

Two-weight criteria of various type for the Hardy-Littlewood maximal operator and singular integrals in variable exponent Lebesgue spaces defined on the real line are established.

Weighted Hardy and singular operators in Morrey spaces

We study the weighted boundedness of the Cauchy singular integral operator $S_\Gm$ in Morrey spaces $L^{p,λ}(\Gm)$ on curves satisfying the arc-chord condition, for a class of "radial type" almost monotonic weights. The non-weighted boundedness is shown to hold on an arbitrary Carleson curve. We show that the weighted boundedness is reduced to the boundedness of weighted Hardy operators in Morrey spaces $L^{p,λ}(0,\ell), \ell>0$. We find conditions for weighted Hardy operators to be bounded in Morrey spaces. To cover the case of curves we also extend the boundedness of the Hardy-Littlewood max…

Dual of Hardy-amalgam spaces and norms inequalities

We characterize the dual spaces of the generalized Hardy spaces defined by replacing Lebesgue quasi-norms by Wiener amalgam ones. In these generalized Hardy spaces, we prove that some classical linear operators such as Calderón-Zygmund, convolution and Riesz potential operators are bounded.

Approximation numbers of composition operators on the Hardy space of the infinite polydisk

We study the composition operators of the Hardy space on D $\infty$ $\cap$ {\ell} 1 , the {\ell} 1 part of the infinite polydisk, and the behavior of their approximation numbers.

Cesaro-Hardy operators on bilateral grand Lebesgue spaces

We obtain in this short article the non-asymptotic estimations for the norm of (generalized) Cesaro-Hardy integral operators in the so-called Bilateral Grand Lebesgue Spaces. We also give examples to show the sharpness of these inequalities.

The boundedness of Fractional Hardy-Littlewood maximal operator on variable lp(Z) spaces using Calderon-Zygmund decomposition

In this paper, we prove strong type, weak type inequalities of Hardy-Littlewood maximal operator and fractional Hardy-Littlewood maximal operator on variable sequence spaces lp(Z). This is achieved using Calderon-Zygmund decomposition for sequences, properties of modular functional and Log Holder continuity.

Weighted local Hardy spaces with variable exponents

This paper defines local weighted Hardy spaces with variable exponent. Local Hardy spaces permit atomic decomposition, which is one of the main themes in this paper. A consequence is that the atomic decomposition is obtained for the functions in the Lebesgue spaces with exponentially decaying exponent. As an application, we obtain the boundedness of singular integral operators, the Littlewood--Paley characterization and wavelet decomposition.

Tent Carleson measures for Hardy spaces

We completely characterize those positive Borel measures $μ$ on the unit ball $\mathbb{B}_ n$ such that the Carleson embedding from Hardy spaces $H^p$ into the tent-type spaces $T^q_ s(μ)$ is bounded, for all possible values of $0<p,q,s<\infty$.

On the boundedness of Hausdorff operators on real Hardy spaces $H^1$ over homogeneous spaces of groups with local doubling property

We give conditions for boundedness of Hausdorff operators on real Hardy spaces $H^1$ over homogeneous spaces of locally compact groups with local doubling property. The special case of the hyperbolic plane is considered.

On vector-valued tent spaces and Hardy spaces associated with non-negative self-adjoint operators

In this paper we study Hardy spaces associated with non-negative self-adjoint operators and develop their vector-valued theory. The complex interpolation scales of vector-valued tent spaces and Hardy spaces are extended to the endpoint p=1. The holomorphic functional calculus of L is also shown to be bounded on the associated Hardy space H^1_L(X). These results, along with the atomic decomposition for the aforementioned space, rely on boundedness of certain integral operators on the tent space T^1(X).

关于Hardy空间的关联空间

On the associated spaces of the Hardy space

本文研究$\mathbb{R}^n$上Hardy空间的关联空间与第二关联空间，给出其刻画，并证明$\textrm{BMO}(\mathbb{R}^n)$空间关联空间的相关结果。

Abstract framework for John Nirenberg inequalities and applications to Hardy spaces

In this paper, we develop an abstract framework for John-Nirenberg inequalities associated to BMO-type spaces. This work can be seen as the sequel of [5], where the authors introduced a very general framework for atomic and molecular Hardy spaces. Moreover, we show that our assumptions allow us to recover some already known John-Nirenberg inequalities. We give applications to the atomic Hardy spaces too.

Products of composition and differentiation operators on the Hardy space

We consider the products of composition and differentiation operators on the Hardy space. We provide a complete characterization of the boundedness and compactness of these operators. Furthermore, we obtain the explicit condition for these operators to be Hilbert-Schmidt operators.

混合径向-角型函数空间上Hardy型算子的一些尖锐界

Some sharp bounds for Hardy type operators on mixed radial-angular type function spaces

本文研究混合径向-角型函数空间上Hardy型算子的尖锐界，并建立分数阶Hardy算子及其共轭算子的尖锐弱型估计。

The Hardy-Littlewood Maximal Operator on Discrete Morrey Spaces

We discuss the Hardy-Littlewood maximal operator on discrete Morrey spaces of arbitrary dimension. In particular, we obtain its boundedness on the discrete Morrey spaces using a discrete version of the Fefferman-Stein inequality. As a corollary, we also obtain the boundedness of some Riesz potentials on discrete Morrey spaces.

A Hardy space analysis of the Báez-Duarte criterion for the RH

In this article, methods from sub-Hardy Hilbert spaces such as the de Branges-Rovnyak spaces and local Dirichlet spaces are used to investigate Báez-Duarte's Hilbert space reformulation of the Riemann hypothesis (RH).

Strong continuity on Hardy spaces

We prove the strong continuity of spectral multiplier operators associated with dilations of certain functions on the general Hardy space $H^1_L$ introduced by Hofmann, Lu, Mitrea, Mitrea, Yan. Our results include the heat and Poisson semigroups as well as the group of imaginary powers.

Weighted Hardy-Littlewood average operators on bilateral grand Lebesgue spaces

We obtain in this short article the non-asymptotic exact estimations for the norm of (generalized) weighted Hardy-Littlewood average integral operator in the so-called Bilateral Grand Lebesgue Spaces. We also give examples to show the sharpness of these inequalities.

Duals of Hardy-amalgam spaces $\mathcal{H}_{\mathrm{loc}}^{(q,p)}$ and Pseudo-differential operators

In this paper, we carry on with the study of the Hardy-Amalgam spaces $\mathcal{H}_{\mathrm{loc}}^{(q,p)}$ spaces introduced in \cite{AbFt}. We investigate their dual spaces and establish some results of boundedness of pseudo-differential operators in these spaces.

A note on Fourier multipliers on the product Hardy spaces

In this article, we present some results about Fourier multipliers on Hardy spaces in the product case. We mainly give descriptions of multipliers from the space $H^1(\mathbb{T}\times\mathbb{T})$ into the space $\ell^2$ and from the space $H^1(\mathbb{R}_+^2\times\mathbb{R}_+^2)$ into the space $L^1$.

Boundedness of $p$-adic Hardy-Hilbert type integral operator on Block spaces

In this paper, we estimate an operator norm of dilation operators on block spaces ($\mathfrak{B}_{r,α}(\mathbb{Q}_p)$) over $p$-adic field. With this estimate, we establish the boundedness of $p$-adic Hardy-Hilbert type integral operator on $\mathfrak{B}_{r,α}(\mathbb{Q}_p)$. Moreover as application to our result, we obtain the $p$-adic Hilbert inequality, $p$-adic Hardy inequality and $p$-adic Hardy-Littlewood-Pólya inequality on $\mathfrak{B}_{r,α}(\mathbb{Q}_p)$.

Hardy-Littlewood inequalities for norms of positive operators on sequence spaces

We consider estimates of Hardy and Littlewood for norms of operators on sequence spaces, and we apply a factorization result of Maurey to obtain improved estimates and simplified proofs for the special case of a positive operator.

Contractive multipliers from Hardy space to weighted Hardy space

It is shown how any contractive multiplier from the Hardy space to a weighted Hardy space $H^{2}_{\bbeta}$ can be factored as a fixed factor composed with the classical Schur multiplier (contractive multiplier between Hardy spaces). The result is applied to get results on interpolation for a Hardy-to-weighted-Hardy contractive multiplier class.

球拟Banach函数空间相关的Hardy空间上的多重线性算子

Multilinear operators on Hardy spaces associated with ball quasi-Banach function spaces

本文证明了多重线性Calderón--Zygmund算子、极大算子及伪微分算子在球拟Banach函数空间相关的（局部）Hardy空间上有界，结果涵盖多种经典空间，显著推广了现有理论。

Duality for symmetric Hardy spaces of noncommutative martingales

We show the dual spaces of conditional Hardy space and symmetric Hardy space of noncommutative martingales. We derive relationship between the symmetric Hardy space of noncommutative martingales and its conditioned version.

Generic versions of a result in the theory of Hardy spaces

For 0<p<1 and f a function in the Hardy space of order p its primitive belongs to the Hardy space q=p/1-p. We show that generically the primitive does not belong, even not locally, in any Hardy space smaller than the Hardy space of order q.

A nested embedding theorem for Hardy-Lorentz spaces with applications to coefficient multiplier problems

We prove a nested embedding theorem for Hardy-Lorentz spaces and use it to find coefficient multiplier spaces of certain non-locally convex Hardy-Lorentz spaces into various target spaces such as Lebesgue sequence spaces, other Hardy spaces, and analytic mixed norm spaces.

Hardy 型空间估计：多线性分数次积分算子

Hardy type spaces estimates for multilinear fractional integral operators

本文证明了多线性分数次积分算子在多种广义 Hardy 空间上的有界性，并推广了现有理论。

Critical Hardy inequality on the half-space via the harmonic transplantation

We prove a critical Hardy inequality on the half-space by using the harmonic transplantation. Also we give an improvement of the subcritical Hardy inequality on the half-space, which converges to the critical Hardy inequality. Sobolev type inequalities are also discussed.

Anisotropic Hardy-Lorentz spaces with variable exponents

In this paper we introduce Hardy-Lorentz spaces with variable exponents associated to dilation in ${\Bbb R}^n$. We establish maximal characterizations and atomic decompositions for our variable exponent anisotropic Hardy-Lorentz spaces.

加权flag和乘积Hardy空间上奇异积分的完全有界性

The complete boundedness of singular integrals on weighted flag and product Hardy space

本文旨在证明奇异积分在加权flag和乘积Hardy空间上的完全有界性，包括单参数奇异积分和flag奇异积分的有界性。

A Montel-type theorem for Hardy spaces of holomorphic functions

We give a version of the Montel theorem for Hardy spaces of holomorphic functions on an infinite dimensional space. As a by-product, we provide a Montel-type theorem for the Hardy space of Dirichlet series. This approach also gives an elementary proof of Montel theorem for the classical one-variable Hardy spaces.

On Hardy spaces of local and nonlocal operators

We characterize conditional Hardy spaces of the Laplacian and of the fractional Laplacian by using Hardy-Stein type identities.

Order boundedness of weighted composition operators on weighted Dirichlet spaces and derivative Hardy spaces

In this paper, we completely characterize the order boundedness of weighted composition operators between different weighted Dirichlet spaces and different derivative Hardy spaces.

On noncommutative weak Orlicz-Hardy spaces

We introduce noncommutative weak Orlicz spaces associated with a weight and study their properties. We also define noncommutative weak Orlicz-Hardy spaces and characterize their dual spaces.

Pointwise multipliers in Hardy-Orlicz spaces, and interpolation

We study multipliers of Hardy-Orlicz spaces $\mH_Φ$ which are strictly contained between $\bigcup_{p>0}H^p$ and so-called ``big'' Hardy-Orlicz spaces. Big Hardy-Orlicz spaces, carrying an algebraic structure, are equal to their multiplier algebra, whereas in classical Hardy spaces $H^p$, the multipliers reduce to $H^{\infty}$. For Hardy-Orlicz spaces $\mH_Φ$ between these two extremal situations and subject to some conditions, we exhibit multipliers that are in Hardy-Orlicz spaces the defining functions of which are related to $Φ$. Even if the results do not entirely characterize the multiplie…

Differences of composition operators between different Hardy spaces

In this paper, we give some estimates for the norm and essential norm of the differences of two composition operators between different Hardy spaces.

The Smoothness of kernel in Hardy spaces

This paper provides a study of problems related to Hardy spaces left by G.\,Weiss in \cite{We}. First, We will prove that the Hardy spaces $H^p(\mathbb{R}^n)$ can be characterized by a fixed Lipschitz function.

Decomposition theorems for Hardy spaces on products of Siegel upper half spaces and bi-parameter Hardy spaces

Products of Siegel upper half spaces are Siegel domains, whose Silov boundaries have the structure of products $\mathscr H_1\times\mathscr H_2$ of Heisenberg groups. By the reproducing formula of bi-parameter heat kernel associated to sub-Laplacians, we show that a function in holomorphic Hardy space $H^1$ on such a domain has boundary value belonging to bi-parameter Hardy space $ H^1 (\mathscr H_1\times \mathscr H_2)$. With the help of atomic decomposition of $ H^1 (\mathscr H_1\times \mathscr H_2)$ and bi-paramete rharmonic analysis, we show that the Cauchy-Szeg\H o projection is a bounded o…

Integration operators between Hardy spaces on the unit ball of $\Cn$

We completely describe the boundedness of the Volterra type operator $J_ g$ between Hardy spaces in the unit ball of $\Cn$. The proof of the one dimensional case used tools, such as the strong factorization for Hardy spaces, that are not available in higher dimensions, and therefore new techniques are developed. In particular, a generalized version of the description of Hardy spaces in terms of the area function is needed.

Triebel-Lizorkin空间中Hardy不等式最佳常数

Best constants for Hardy inequalities in Triebel--Lizorkin spaces

本文研究了Triebel-Lizorkin空间中分数Hardy不等式最佳常数的问题，推广了加权分数Hardy不等式并给出了新的结果。

Weighted composition operators between weighted Hardy spaces on rooted trees

In this paper, we introduce a discrete analogue of weighted Hardy spaces on rooted trees and study weighted composition operators between them in detail. In particular, we characterize bounded and compact weighted composition operators between discrete Hardy spaces. We also consider isometric weighted composition operators between these spaces.

Compact embedding derivatives of Hardy spaces into Lebesgue spaces

We characterize the positive Borel measures such that the differentiation operator of order $n\in\mathbb{N}\cup\{0\}$ is compact from the Hardy space $H^p$ into $L^q(μ)$, $0<p,q<\infty$.