Related papers: Haar Type and Carleson Constants

We consider decoupling inequalities for random variables taking values in a Banach space $X$. We restrict the class of distributions that appear as conditional distributions while decoupling and show that each adapted process can be…

The paper considers a general concept of dichotomy with different growth rates for linear discrete-time systems in Banach spaces. Characterizations in terms of Lyapunov type sequences of norms are given. The approach is illustrated by…

In [1], Y. Belov, K. Seip, and the author studied the Carleson measures for certain spaces of analytic functions of which the de Branges spaces and the model subspaces of the Hardy space H2 are the prime examples. In this paper, we continue…

We consider the class of weakly porous sets in Euclidean spaces. As our main goal, we give a precise characterization in terms of dyadic covering of these sets. Also, we obtain the Carleson embedding inequality for porous sets.

We characterize the Carleson measures $\mu$ on the unit disk for which the image of the Hardy space $H^p$ under the corresponding embedding operator is closed in $L^p(\mu)$. In fact, a more general result involving $(p,q)$-Carleson measures…

We investigate possible quantifications of the Banach-Saks property and the weak Banach-Saks property. We prove quantitative versions of relationships of the Banach-Saks property of a set with norm compactness and weak compactness. We…

In this paper, by describing characterizations of Carleson type measures on $[0,1)$, we determine the range of a Ces\`aro-like operator acting on $H^\infty$. A special case of our result gives an answer to a question posed by P.…

The theory of Carleson measures, stopping time arguments, and atomic decompositions has been well-established in harmonic analysis. More recent is the theory of phase space analysis from the point of view of wave packets on tiles, tree…

The concept of Rademacher type $p$ ($1\leq p\leq2$) plays an important role in the local theory of Banach spaces. In \cite{mas88} Mascioni considers a weakening of this concept and shows that for a Banach space $X$ weak Rademacher type $p$…

We analyse several examples of separable Banach spaces, some of them new, and relate them to several dichotomies obtained in the previous paper Banach spaces without minimal subspaces, by classifying them according to which side of the…

We prove a variation norm Carleson theorem for Walsh-Fourier series of functions with values in a UMD Banach space. Our only hypothesis on the Banach space is that it has finite tile-type, a notion introduced by Hyt\"onen and Lacey. Given q…

We extend Carleson's formula to radially polynomially weighted Dirichlet spaces.

This article provides a concise introduction to the theory of Haar measures on locally compact Hausdorff groups. We cover the necessary preliminaries on topological groups and measure theory, the Haar correspondence, unimodularity and Haar…

We give a capacitary type characterization of Carleson measures for a class of Hardy-Sobolev spaces (also known as weighted Dirichlet spaces) on the Siegel upper half-space, introduced by Arcozzi et al. This answers in part a question…

In this paper we explore conditions on variable symbols with respect to Haar systems, defining Calder\'on-Zygmund type operators with respect to the dyadic metrics associated to the Haar bases.We show that Petermichl's dyadic kernel can be…

We define a scale of L^q Carleson norms, all of which characterize the membership of a function in BMO. The phenomenon is analogous to the John-Nirenberg inequality, but on the level of Carleson measures. The classical Carleson condition…

Let $p(\cdot):\ {\mathbb{R}^n}\to(0,\infty)$ be a variable exponent function satisfying the globally log-H\"{o}lder continuous condition and $A$ a general expansive matrix on ${\mathbb{R}^n}$. In this article, the authors introduce the…

In this paper, the Hadamard-Bergman convolution and Banach algebra structure by the Duhamel product on Hardy-Carleson type tent spaces was investigated. Moreover, the boundedness and compactness of the Ces\`aro-like operator…

In this paper first we define generalized Carleson mea- sure. Then we consider a special case of it, named conditional Carleson measure on the Bergman spaces. After that we give a characterization of conditional Carleson measures on Bergman…

We characterize the Carleson measures for the Drury-Arveson Hardy space and other Hilbert spaces of analytic functions of several complex variables. This provides sharp estimates for Drury's generalization of Von Neumann's inequality. The…