Related papers: Carleson measures on simply connected domains

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…

Carleson measures are ubiquitous in Harmonic Analysis. In the paper of Fefferman--Kenig--Pipher in 1991 an interesting class of Carleson measures was introduced for the need of regularity problems of elliptic PDE. These Carleson measures…

We prove that, for every $\alpha > -1$, the pull-back measure $\phi ({\cal A}_\alpha)$ of the measure $d{\cal A}_\alpha (z) = (\alpha + 1) (1 - |z|^2)^\alpha \, d{\cal A} (z)$, where ${\cal A}$ is the normalized area measure on the unit…

We consider weighted harmonic Bergman spaces on upper half-space with weights depending only on the vertical coordinate. In these settings, we give full asymptotic expansion of weighted harmonic Bergman kernel as well as full asymptotic…

We study the Hausdorff dimension of a measure related to a positive weak solution of a certain partial differential equation in a simply connected domain in the plane. Our work generalizes work of Lewis and coauthors when the measure is $p$…

In this paper we will show how the boundedness condition for the weighted composition operators on a class of spaces of analytic functions on the open right complex half-plane called Zen spaces (which include the Hardy spaces and weighted…

We investigate when the Bergman metric of a bounded domain is, up to a constant factor $\lambda$, induced by the Bergman metric of a finite-dimensional unit ball $\mathbb{B}^N$ via a holomorphic isometric immersion. For a strictly…

Let $D$ be a domain in the complex plane $\mathbb{C}$. The Hardy number of $D$, which first introduced by Hansen, is the maximal number $h(D)$ in $[0,+\infty]$ such that $f$ belongs to the classical Hardy space $H^p (\mathbb{D})$ whenever…

We prove necessary and sufficient integral conditions involving extremal distance for a conformal mapping of the unit disk to belong to the Hardy or weighted Bergman spaces. We also give characterizations for the Hardy number and the…

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…

It is shown that the property of being bounded below (having closed range) of weighted composition operators on Hardy and Bergman spaces can be tested by their action on a set of simple test functions, including reproducing kernels. The…

We construct a one parameter family of integral transforms connecting the classical Hardy space with a class of weighted Bergman spaces called Barut-Girardello spaces.

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.

In this paper we formulate embedding maps into time-frequency space related to the Carleson operator and its variational counterpart. We prove bounds for these embedding maps by iterating the outer measure theory of [DT15]. Introducing…

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…

For $0<p<\infty$, $\Psi:[0,\infty)\to(0,\infty)$ and a finite positive Borel measure $\mu$ on the unit disc $\mathbb{D}$, the Lebesgue--Zygmund space $L^p_{\mu,\Psi}$ consists of all measurable functions $f$ such that $\lVert f…

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…

We establish the boundedness of the multilinear Calder\'on-Zygmund operators from a product of weighted Hardy spaces into a weighted Hardy or Lebesgue space. Our results generalize to the weighted setting results obtained by Grafakos and…

For a bounded domain $D \subset \mathbb{C}^n$, let $K_D = K_D(z) > 0$ denote the Bergman kernel on the diagonal and consider the reproducing kernel Hilbert space of holomorphic functions on $D$ that are square integrable with respect to the…

We define Hardy spaces $\mathcal{H}^p$ for quasiregular mappings in the plane, and show that for a particular class of these mappings many of the classical properties that hold in the classical setting of analytic mappings still hold. This…