Related papers: $H^{\infty}$ interpolation and embedding theorems …

We find sufficient conditions for a discrete sequence to be interpolating or sampling for certain generalized Bergman spaces on open Riemann surfaces. As in previous work of Bendtsson, Ortega-Cerda, Seip, Wallsten and others, our conditions…

We solve an interpolation problem in $A^p_\alpha$ involving specifying a set of (possibly not distinct) $n$ points, where the $k^{\textrm{th}}$ derivative at the $k^{\textrm{th}}$ point is up to a constant as large as possible for functions…

Given a finite set \sigma of the unit disc \mathbb{D}={z\in\mathbb{C}:, |z|<1} and a holomorphic function f in \mathbb{D} which belongs to a class X, we are looking for a function g in another class Y (smaller than X) which minimizes the…

Inner functions play a central role in function theory and operator theory on the Hardy space over the unit disk. Motivated by recent works of C. B\'en\'eteau et al. and of D. Seco, we discuss inner functions on more general weighted Hardy…

We prove norm estimates for multilinear fractional integrals acting on weighted and variable Hardy spaces. In the weighted case we develop ideas we used for multilinear singular integrals [7]. For the variable exponent case, a key element…

We study weighted $H^\infty$ spaces of analytic functions on the open unit disc in the case of non-doubling weights, which decrease rapidly with respect to the boundary distance. We characterize the solid hulls of such spaces and give quite…

It is well known that real measures on the circle are characterized by their Herglotz transform, an analytic function in the unit disc. Invariance of the measure under N-multiplication translates into a functional equation for the Herglotz…

We study Clark measures associated with general two-variable rational inner functions (RIFs) on the bidisk, including those with singularities, and with general $d$-variable rational inner functions with no singularities. We give precise…

We determine the solid hull and solid core of weighted Banach spaces $H_v^\infty$ of analytic functions $f$ such that $v|f|$ is bounded, both in the case of the holomorphic functions on the disc and on the whole complex plane, for a very…

We study embeddings associated with oscillation functionals in rearrangement-invariant spaces. More precisely, given a positive function \(\psi\), we analyze how the interaction between the geometry of the underlying space and the growth of…

An indefinite generalization of Nudel'man's problem is used in a systematic approach to interpolation theorems for generalized Schur and Nevanlinna functions with interior and boundary data. Besides results on existence criteria for…

We analyse the 3-extremal holomorphic maps from the unit disc $\mathbb{D}$ to the symmetrised bidisc $ \mathcal{G}$, defined to be the set $ \{(z+w,zw): z,w\in\mathbb{D}\}$, with a view to the complex geometry and function theory of…

Let $\mathcal{D}$ be the class of radial weights on the unit disk which satisfy both forward and reverse doubling conditions. Let $g$ be an analytic function on the unit disk $\mathbb{D}$. We characterize bounded and compact Volterra type…

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…

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.

In this paper we study sharp pointwise inequalities for maximal operators. In particular, we strengthen DeVore's inequality for the moduli of smoothness and a logarithmic variant of Bennett--DeVore--Sharpley's inequality for rearrangements.…

By a regular embedding of a graph K in a surface we mean a 2-cell embedding of K in a compact connected surface such that the automorphism group acts regularly on flags. In this paper, we classify the nonorientable regular embeddings of the…

We obtain a compact Sobolev embedding for $H$-invariant functions in compact metric-measure spaces, where $H$ is a subgroup of the measure preserving bijections. In Riemannian manifolds, $H$ is a subgroup of the volume preserving…

We prove compactness of the embeddings in Sobolev spaces for fractional super and sub harmonic functions with radial symmetry. The main tool is a pointwise decay for radially symmetric functions belonging to a function space defined by…

This paper studies the determining sets for analytic functions from the symmetrized bidisk into the open unit disk in $\mathbb C$. It relates the idea to the uniqueness of the solutions of a Nevanlinna-Pick interpolation problem. It also…