Anisotropic Herz-type Hardy spaces with variable exponent and their applications
type: Item
instance of: scholarly article
title: Anisotropic Herz-type Hardy spaces with variable exponent and their applications
zbMATH Open document ID: 1413.42045
published in: Acta Mathematica Hungarica
publication date: 2019-02-01T00:00:00Z
review text: More and more classical spaces are generalized to the setting with variable exponent. In the paper under review, a class of anisotropic Herz-type Hardy spaces with variable exponent associated with a non-isotropic dilation on \(\mathbb R^n\) is introduced, and characterizations of these spaces are established in terms of atomic and molecular decompositions. As a preceding source for anisotropic Hardy type spaces in a ``usual'' metric, Bownik's work is righteously referred to. It is also worth adding \textit{S. Dekel} and \textit{T. Weissblat} [Math. Nachr. 285, No. 17--18, 2078--2092 (2012; Zbl 1261.42032)] The obtained results are applied to show that these Herz-type Hardy spaces are a proper substitute for earlier studied Herz-type spaces with variable exponent. Further, interpolation of operators on the anisotropic Herz-type Hardy spaces with variable exponent is discussed.
reviewed by: Elijah Liflyand
Mathematics Subject Classification ID: 42B30
Mathematics Subject Classification ID: 42B35
Mathematics Subject Classification ID: 46E30
zbMATH DE Number: 7011032
zbMATH Keywords: anisotropic Herz-type Hardy space
zbMATH Keywords: variable exponent
zbMATH Keywords: atomic decomposition
zbMATH Keywords: molecular decomposition
zbMATH Keywords: interpolation
author: Huan Zhao
author: Jiang Zhou
MaRDI profile type: Publication
full work available at URL: s10474-018-0851-6
OpenAlex ID: W2809845067
DOI: 10.1007/S10474-018-0851-6
description: scientific article; zbMATH DE number 7011032