Related papers: Compact Carleson measures from sparse sequences
Doubling metric measure spaces provide a natural framework for singular integral operators. In contrast, the study of maximally modulated singular integral operators, the so-called Carleson operators, has largely been limited to Euclidean…
Hardy space theory has been studied on manifolds or metric measure spaces equipped with either Gaussian or sub-Gaussian heat kernel behaviour. However, there are natural examples where one finds a mix of both behaviour (locally Gaussian and…
Let $S$ be a sequence of points in ${\mathbb{D}}^{n}.$ Suppose that $S$ is $H^{p}$ interpolating. Then we prove that the sequence $S$ is Carleson, provided that $p>2.$ We also give a sufficient condition, in terms of dual boundedness and…
In this note we continue giving the characterisation of weights for two-weight Hardy inequalities to hold on general metric measure spaces possessing polar decompositions. Since there may be no differentiable structure on such spaces, the…
In this paper, we investigate the two-weight Hardy inequalities on metric measure space possessing polar decompositions for the case $p=1$ and $1 \leq q <\infty.$ This result complements the Hardy inequalities obtained in \cite{RV} in the…
This paper can be considered as the sequel of [6], where the authors have proposed an abstract construction of Hardy spaces H^1. They shew an interpolation result for these Hardy spaces with the Lebesgue spaces. Here we describe a more…
We characterize the Carleson measures for an exponential Bergman space on the unit ball of $\mathbb C^n$ in terms of the ball induced by the complex Hessian of the logarithm of the weight function. The boundedness (or compactness) of…
We characterize using the Bergman kernel Carleson measures of Bergman spaces in strongly pseudoconvex bounded domains in several complex variables, generalizing to this setting theorems proved by Duren and Weir for the unit ball. We also…
We study conditions for containment of a given space $X$ of analytic functions on the unit disk $\mathbb{D}$ in the de Branges-Rovnyak space $\mathcal{H}(b)$. We deal with the non-extreme case in which $b$ admits a Pythagorean mate $a$, and…
It follows, from a generalised version of Paley-Wiener theorem, that the Laplace transform is an isometry between certain spaces of weighted $L^2$ functions defined on $(0, \infty)$ and (Hilbert) spaces of analytic functions on the right…
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…
We obtain characterizations of positive Borel measures $\mu$ on $\B^n$ so that some weighted Hardy-Sobolev are imbedded in $L^p(d\mu)$, where $w$ is an $A_p$ weight in the unit sphere of $\C^n$.
Boundedness of an abstract formulation of Hardy operators between Lebesgue spaces over general measure spaces is studied and, when the domain is L^1, shown to be equivalent to the existence of a Hardy inequality on the half line with…
We introduce and study Hankel operators defined on the Hardy space of regular functions of a quaternionic variable. Theorems analogous to those of Nehari anc C. Fefferman are proved.
We consider the Carleson embeddings of the classical Hardy spaces (on the disk) into a L p ($\mu$) space, where $\mu$ is a Carleson measure on the unit disk. This includes the case of composition operators. We characterize such operators…
In this paper, we characterize Carleson measure and vanishing Carleson measure on Bergman spaces with admissible weights in terms of {\it t-Berezin transform} and {\it averaging function} as key tools. Moreover, power bounded and power…
As outlined below, this paper is devoted to a Carleson-type-measure-based study of the holomorphic Campanato $2$-space on the open unit ball $\mathbb B_n$ of $\mathbb C^n$, comprising all Hardy $2$-functions whose oscillations in…
We investigate composition operators on Hardy-Orlicz spaces when the Orlicz function $\Psi$ grows rapidly: compactness, weak compactness, to be $p$-summing, order bounded,..., and show how these notions behave according to the growth of…
For $0<s<1$, let $\{z_n\}$ be a sequence in the open unit disk such that $\sum_n (1-|z_n|^2)^s \delta_{z_n}$ is an $s$-Carleson measure. In this paper, we consider the connections between this $s$-Carleson measure and the theory of M\"obius…
This work explores several aspects of interpolating sequences for $\ell^p_A$, the space of analytic functions on the unit disk with $p$-summable Maclaurin coefficients. Much of this work is communicated through a Carlesonian lens. We…