Molecular characterization of weak Hardy spaces associated with ball quasi-Banach function spaces on spaces of homogeneous type with its applications to Littlewood-Paley function characterizations
type: Item
instance of: scholarly article
title: Molecular characterization of weak Hardy spaces associated with ball quasi-Banach function spaces on spaces of homogeneous type with its applications to Littlewood-Paley function characterizations
zbMATH Open document ID: 1504.42077
author: Jingsong Sun
author: Wen Yuan
author: Dachun Yang
published in: Forum Mathematicum
publication date: 2022-11-04T00:00:00Z
review text: Let \((\mathbb X,d,\mu)\) be a space of homogeneous type in the sense of \textit{R. R. Coifman} and \textit{G. Weiss} [Analyse harmonique non-commutative sur certains espaces homogènes. Etude de certaines intégrales singulières. (Non-commutative harmonic analysis on certain homogeneous spaces. Study of certain singular integrals.). Springer, Cham (1971; Zbl 0224.43006)], and \(X(\mathbb X)\) a ball quasi-Banach function space on \(\mathbb X\). In this paper under review, the authors introduce and study the weak Hardy space on spaces of homogeneous type in the sense of Coifman and Weiss. They first introduce the weak Hardy space \(\widetilde{WH}_X(\mathbb X)\) associated with \(X(\mathbb X)\) by using the Lusin area function. Then the molecule characterization, the grand maximal function characterization, and the Littlewood-Paley \(g\)-function and \(g_\lambda^\ast\)-function characterization of the weak Hardy space are obtained in this paper. As applications, they apply the above results to the Lebesgue space, the weighted Lebesgue space, the Orlicz space, and the variable Lebesgue space. We remark that the main results of this paper are also new in the weighted Lebesgue spaces, Orlicz spaces, and variable Lebesgue spaces.
reviewed by: Jian Tan
Mathematics Subject Classification ID: 42B30
Mathematics Subject Classification ID: 42B25
Mathematics Subject Classification ID: 42B35
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 30L99
zbMATH DE Number: 7612316
zbMATH Keywords: space of homogeneous type
zbMATH Keywords: ball quasi-Banach function space
zbMATH Keywords: weak Hardy space
zbMATH Keywords: maximal function
zbMATH Keywords: molecule
zbMATH Keywords: weak tent space
zbMATH Keywords: Littlewood-Paley function
MaRDI profile type: Publication
full work available at URL: forum-2022-0074
OpenAlex ID: W4297999539
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DOI: 10.1515/FORUM-2022-0074

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