Variable anisotropic Hardy spaces with variable exponents
type: Item
instance of: scholarly article
title: Variable anisotropic Hardy spaces with variable exponents
zbMATH Open document ID: 1479.42065
author: Zhenzhen Yang
author: Yajuan Yang
author: Jiawei Sun
author: Baode Li
published in: Analysis and Geometry in Metric Spaces
publication date: 2021-09-10T00:00:00Z
review text: Let \(\Theta\) be a continuous ellipsoid consisting of ellipsoids \(\theta_{x,t}\) with center \(x\in \mathbb{R}^n\) and scale \(t\in \mathbb{R}\) of the form \(\theta_{x,t}={M}_{x,t}(\mathbb{B}_n)+x\), where \({M}_{x,t}\) is a nonsingular matrix and \(\mathbb{B}_n\) is the unit ball in \(\mathbb{R}^n\). Let \(p(\cdot): \mathbb{R}^n \to (0,\infty]\) be a variable exponent function satisfying the globally log-Hölder continuous condition. The main aim of the paper is to develop the theory of highly geometric Hardy spaces \(H^{p(\cdot)}(\Theta)\). Similarly to classical results, the authors characterize the Hardy space \(H^{p(\cdot)}(\Theta)\) via the radial grand maximal function and the atomic decomposition. As an application, they establish a number of criteria for a singular integral to be bounded from \(H^{p(\cdot)}(\Theta)\) to \(L^{p(\cdot)}(\Theta)\) and bounded on \(H^{p(\cdot)}(\Theta)\).
Mathematics Subject Classification ID: 42B35
Mathematics Subject Classification ID: 42B30
Mathematics Subject Classification ID: 42B25
Mathematics Subject Classification ID: 42B20
zbMATH DE Number: 7394293
zbMATH Keywords: Hardy space
zbMATH Keywords: continuous ellipsoid cover
zbMATH Keywords: maximal function
zbMATH Keywords: atomic decomposition
zbMATH Keywords: singular integral operator
reviewed by: Bui The Anh
MaRDI profile type: Publication
full work available at URL: agms-2020-0124
OpenAlex ID: W3184822608
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DOI: 10.1515/AGMS-2020-0124
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description: scientific article; zbMATH DE number 7394293