Related papers: Berezin transforms on modified Bergman spaces

There has been a great deal of work done in recent years on weighted Bergman spaces $\apa$ on the unit ball $\bn$ of $\cn$, where $0<p<\infty$ and $\alpha>-1$. We extend this study in a very natural way to the case where $\alpha$ is {\em…

Dual pairs of interior and exterior Hardy spaces associated to a simple closed Lipschitz planar curve are considered, leading to a M\"obius invariant function bounding the norm of the Cauchy transform $\bf{C}$ from below. This function is…

We construct a uniformly expanding map of the interval, preserving Lebesgue measure, such that the corresponding transfer operator admits a spectral gap on the space of Lipschitz functions, but does not act continuously on the space of…

In this note we show how to adjust some proofs of Koskela et. al 2003 and Jiang 2011 in order to show that in certain spaces $(X,d,\mu)$, like $RCD(K,N)$-spaces, every Sobolev function with local $L^{p}$-Laplacian and $p>\dim\mu$ is locally…

We study a question of density of Lipschitz mappings in the Sobolev class of mappings from a closed manifold into a singular space. The main result of the paper shows that if we change the metric in the target space to a bi-Lipschitz…

Let $D$ be a nonempty open set in a metric space $(X,d)$ with $\partial D\neq \emptyset$. Define \begin{equation*} h_{D,c}(x,y)=\log\left(1+c\frac{d(x,y)}{\sqrt{d_D(x)d_D(y)}}\right), \end{equation*} where $d_D(x)=d(x,\partial D)$ is the…

Given a metric space (X, d), we continue our study of the distance function x\mapsto d(x,-) and its relation to bi-Lipschitz embeddings of (X, d) into R^N. As application, given a compact metric-measure space (X, d,\mu), we give three…

The linearized Bregman iterations (LBreI) and its variants have received considerable attention in signal/image processing and compressed sensing. Recently, LBreI has been extended to a larger class of nonconvex functions, along with…

We show that every real-valued Lipschitz function on a subset of a metric space can be extended to the whole space while preserving the slope and, up to a small error, the global Lipschitz constant. This answers a question posed by Di…

In this article, we consider the H\"{o}lder continuity of injective maps in Orlicz-Sobolev classes defined on the unit ball. Under certain conditions on the growth of dilatations, we obtain the H\"{o}lder continuity of the indicated class…

We employ Besov space techniques and the method of modulus of continuity to obtain the global well-posedness of the modified Porous Media Equation.

We prove sharp remainder bounds for the Berezin-Toeplitz quantization and present applications to semiclassical quantum measurements.

We present a detailed survey of recent developments in the study of the finite Hilbert transform and its corresponding inversion problem in rearrangement invariant spaces on $(-1,1)$.

This short note contains an elementary observation in response to the recent posting arXiv:1707.06593v1, which studies the Lipschitz extension modulus to $n$ additional points. We bound this modulus in terms of the well-studied Lipschitz…

In this paper we study the compactness of operators on the Bergman space of the unit ball and on very generally weighted Bargmann-Fock spaces in terms of the behavior of their Berezin transforms and the norms of the operators acting on…

We give a probabilistic characterisation of the Besov-Lipschitz spaces $Lip(\alpha,p,q)(X)$ on domains which support a Markovian kernel with appropriate exponential bounds. This extends former results of \cite{Jon,KPP1,KPP2,GHL} which were…

We study the long-time behavior of almost periodic solutions to stochastic scalar conservation laws in any space dimension, under the assumption of Lipschitz continuity of the flux functions and a non-degeneracy condition. We show the…

We show that, for Finsler spaces with cubic metric, Landsberg spaces are Berwaldian. Also, for decomposable metrics, we determine specific conditions for a space with cubic metric to be of Berwald type, thus refining the result in [6].

We completely describe spaces of multipliers of certain harmonic function spaces of Bergman type in R^n.This is the first sharp result of this kind for Bergman type mixed norm spaces of harmonic functions in the unit ball of R^n

We provide some necessary and sufficient conditions for a proper lower semicontinuous convex function, defined on a real Banach space, to be locally or globally Lipschitz continuous. Our criteria rely on the existence of a bounded selection…