Bourgain-Morrey spaces and their applications to boundedness of operators
type: Item
instance of: scholarly article
title: Bourgain-Morrey spaces and their applications to boundedness of operators
author: Naoya Hatano
author: Toru Nogayama
author: Yoshihiro Sawano
author: Denny Ivanal Hakim
published in: Journal of Functional Analysis
publication date: 2022-11-15T00:00:00Z
review text: In this paper, the authors study the so-called Bourgain-Morrey spaces. Precisely, the authors study the fundamental properties of the Bourgain-Morrey space, including approximation and interpolation properties. Moreover, the boundedness of operators, such as the Hardy-Littlewood maximal operator, fractional integral operators, fractional maximal operators, and singular integral operators, on the Bourgain-Morrey space is also established. In particular, the embedding result by \textit{P. Bégout} and \textit{A. Vargas} [Trans. Am. Math. Soc. 359, No. 11, 5257--5282 (2007; Zbl 1171.35109)] is refined. Furthermore, the authors describe the dual of Bourgain-Morrey spaces and combine this with existing results to conclude the reflexivity of these spaces.
Mathematics Subject Classification ID: 42B35
Mathematics Subject Classification ID: 42B20
Mathematics Subject Classification ID: 42B25
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 46B70
Mathematics Subject Classification ID: 26A33
zbMATH DE Number: 7616871
zbMATH Keywords: Bourgain-Morrey spaces
zbMATH Keywords: fractional integral operators
zbMATH Keywords: singular integral operators
zbMATH Keywords: duality
reviewed by: Sibei Yang
MaRDI profile type: Publication
full work available at URL: j.jfa.2022.109720
OpenAlex ID: W4296175772
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DOI: 10.1016/J.JFA.2022.109720
description: scientific article; zbMATH DE number 7616871