Benoit F. Sehba
We prove Carleson embeddings for Bergman-Orlicz spaces of the unit ball that extend the lower triangle estimates for the usual Bergman spaces.
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For $\mathbb B^n$ the unit ball of $\mathbb C^n$, we consider Bergman-Orlicz spaces of holomorphic functions in $L^Φ_α(\mathbb B^n)$, which are generalizations of classical Bergman spaces. We obtain atomic decomposition for functions in the Bergman-Orlicz space $\mathcal A^Φ_α(\mathbb B^n)$ where $Φ$ is either convex or concave growth function. We then prove weak factorization theorems involving the Bloch space and a Bergman-Orlicz space and also weak factorization theorems involving two Bergman-Orlicz spaces.
In this paper we characterize off-diagonal Carleson embeddings for both Hardy-Orlicz spaces and Bergman-Orlicz spaces of the upper-half plane. We use these results to obtain embedding relations and pointwise multipliers between these spaces.
We define the notion of $Φ$-Carleson measures where $Φ$ is either a concave growth function or a convex growth function and provide an equivalent definition. We then characterize $Φ$-Carleson measures for Bergman-Orlicz spaces, and apply them to characterize multipliers between Bergman-Orlicz spaces.
Carleson embeddings and pointwise multipliers between Hardy-Orlicz spaces and Bergman-Orlicz spaces of the upper half-plane
本文给出涉及凹或凸增长函数的 Carleson 测度的一般刻画，并据此建立上半平面 Hardy-Orlicz 空间与 Bergman-Orlicz 空间之间的连续嵌入与逐点乘子集合的刻画。
We prove Carleson embeddings for Bergman spaces of tube domains over symmetric cones, we apply them to characterize symbols of bounded Cesàro-type operators from weighted Bergman spaces to weighted Besov spaces. We also obtain Schatten class criteria of Toeplitz operators and Cesàro-type operators on weighted Hilbert-Bergman spaces.
It is well known that a function is in a Bergman space of the unit ball if and only if it satisfies some Hardy-type inequalities. We extend this fact to Bergman-Orlicz spaces. As applications, we obtain Gustavsson-Peetre interpolation of two Bergman-Orlicz spaces and we completely characterize symbols of bounded or compact Cesàro-type operators on Bergman-Orlicz spaces, extending known results for classical weighted Bergman spaces.
Atomic decomposition of Bergman-Orlicz space on the upper complex half-plane
本文提出上半复平面上Bergman-Orlicz空间的原子分解，用于刻画带损失的Carleson嵌入并控制复合算子。
For $\mathbb B^n$ the unit ball of $\mathbb C^n$, we consider Bergman-Orlicz spaces of holomorphic functions in $L^Φ_α$, which are generalizations of classical Bergman spaces. We characterize the dual space of large Bergman-Orlicz space, and bounded Hankel operators between some Bergman-Orlicz spaces $A_α^{Φ_1}(\mathbb B^n)$ and $A_α^{Φ_2}(\mathbb B^n)$ where $Φ_1$ and $Φ_2$ are either convex or concave growth functions.
The purposes of this paper are two fold. First, we extend the method of non-homogeneous harmonic analysis of Nazarov, Treil and Volberg to handle "Bergman--type" singular integral operators. The canonical example of such an operator is the Beurling transform on the unit disc. Second, we use the methods developed in this paper to settle the important open question about characterizing the Carleson measures for the Besov--Sobolev space of analytic functions $B^σ_2$ on the complex ball of $\mathbb{C}^d$. In particular, we demonstrate that for any $σ> 0$, the Carleson measures for the space are ch…
This paper gives embedding theorems for a very general class of weighted Bergman spaces: the results include a number of classical Carleson embedding theorems as special cases. We also consider little Hankel operators on these Bergman spaces. Next, a study is made of Carleson embeddings in the right half-plane induced by taking the Laplace transform of functions defined on the positive half-line (these embeddings have applications in control theory): particular attention is given to the case of a sectorial measure or a measure supported on a strip, and complete necessary and sufficient conditi…
In the setting of tube domains over symmetric cones, $T_Ω$, we study the characterization of the positive Borel measures $μ$ for which the Hardy space $H^p$ is continuously embedded into the Lebesgue space $L^q (T_Ω, dμ)$, $0<p<q<\infty.$ Extending a result due to Blasco for the unit disc, we reduce the problem to standard measures. We obtain that a Hardy space $H^{p}$, $1\leq p < \infty,$ embeds continuously in weighted Bergman spaces with larger exponents. Finally we use this result to characterize multipliers from $H^{2m}$ to Bergman spaces for every positive integer $m$.
We prove that, for every $α> -1$, the pull-back measure $ϕ({\cal A}_α)$ of the measure $d{\cal A}_α(z) = (α+ 1) (1 - |z|^2)^α\, d{\cal A} (z)$, where ${\cal A}$ is the normalized area measure on the unit disk $\D$, by every analytic self-map $ϕ\colon \D \to \D$ is not only an $(α+ 2)$-Carleson measure, but that the measure of the Carleson windows of size $\eps h$ is controlled by $\eps^{α+ 2}$ times the measure of the corresponding window of size $h$. This means that the property of being an $(α+ 2)$-Carleson measure is true at all infinitesimal scales. We give an application by characterizing…
In this note, we obtain a full characterization of radial Carleson measures for the Hilbert-Hardy space on tube domains over symmetric cones. For large derivatives, we also obtain a full characterization of the measures for which the corresponding embedding operator is continuous. Restricting to the case of light cones of dimension three, we prove that by freezing one or two variables, the problem of embedding derivatives of the Hilbert-Hardy space into Lebesgue spaces reduces to the characterization of Carleson measures for Hilbert-Bergman spaces of the upper-half plane or the product of two …
Carleson-type embeddings with closed range
研究Carleson测度μ下Hardy空间H^p在L^p(μ)中的像是否闭合，并推广至(p,q)-Carleson测度及Bergman空间。
Refined Two Weight Estimates for the Bergman Projection
该研究针对单位球上Bergman投影的双权有界性问题，分别基于权的Orlicz平均与混合$B_{\infty}$-$B_2$特征，证明了两类充分条件，推进了相关调和分析领域的双权估计研究。
In this paper, we study the behavior of the weighted composition operators acting on Bergman spaces defined on strictly pseudoconvex domains via the sparse domination technique from harmonic analysis. As a byproduct, we also prove a weighted type estimate for the weighted composition operators which is adapted to Sawyer-testing conditions. Our results extend the work by the first author, Li, Shi and Wick under a much more general setting.
On the Bourgain--Brezis--Mironescu spaces over Carleson tents
通过上 Carleson 帐篷上的平均振荡引入 Bourgain–Brezis–Mironescu 空间的 Carleson 类似物，证明其包含多种函数类并建立分解，进一步在迹的层面上证明刚性定理。
Let $φ: \mathbb R^n\times [0,\infty)\to[0,\infty)$ be such that $φ(x,\cdot)$ is an Orlicz function and $φ(\cdot,t)$ is a Muckenhoupt $A_\infty(\mathbb R^n)$ weight uniformly in $t$. In this article, the authors introduce the Musielak-Orlicz Campanato space ${\mathcal L}_{φ,q,s}({\mathbb R}^n)$ and, as an application, prove that some of them is the dual space of the Musielak-Orlicz Hardy space $H^φ(\mathbb R^n)$, which in the case when $q=1$ and $s=0$ was obtained by L. D. Ky [arXiv: 1105.0486]. The authors also establish a John-Nirenberg inequality for functions in ${\mathcal L}_{φ,1,s}({\math…
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…
Convexity of the embedding parameter sets of some analytic function spaces
研究加权Bergman-Orlicz空间连续嵌入参数集的几何结构，证明在特定对数凸性和对数凹性条件下，可接受的权重指数集为凸集，并探讨其对偶问题。
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 $L$ be the divergence form elliptic operator with complex bounded measurable coefficients, $ω$ the positive concave function on $(0,\infty)$ of strictly critical lower type $p_\oz\in (0, 1]$ and $ρ(t)={t^{-1}}/ω^{-1}(t^{-1})$ for $t\in (0,\infty).$ In this paper, the authors study the Orlicz-Hardy space $H_{ω,L}({\mathbb R}^n)$ and its dual space $\mathrm{BMO}_{ρ,L^\ast}({\mathbb R}^n)$, where $L^\ast$ denotes the adjoint operator of $L$ in $L^2({\mathbb R}^n)$. Several characterizations of $H_{ω,L}({\mathbb R}^n)$, including the molecular characterization, the Lusin-area function characte…
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…
We prove a Fredholm criterion for operators in the Banach algebra of singular integral operators with matrix piecewise continuous coefficients acting on a variable Lebesgue space with a radial oscillating weight over a logarithmic Carleson curve. The local spectra of these operators are massive and have a shape of spiralic horns depending on the value of the variable exponent, the spirality indices of the curve, and the Matuszewska-Orlicz indices of the weight at each point. These results extend (partially) the results of A. Böttcher, Yu. Karlovich, and V. Rabinovich for standard Lebesgue spac…
Anisotropic Ball Campanato-Type Function Spaces and Their Applications
本文引入与扩张矩阵和球拟 Banach 函数空间相关的各向异性球 Campanato 型空间，证明其对偶关系并给出 Littlewood–Paley、Carleson 测度等刻画。
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