The preduals of Banach space valued Bourgain–Morrey spaces

IF 1 3区数学 Q1 MATHEMATICS

Annals of Functional Analysis Pub Date : 2025-08-04 DOI:10.1007/s43034-025-00458-w

Tengfei Bai, Pengfei Guo, Jingshi Xu

引用次数: 0

Abstract

Let X be a Banach space such that there exists a Banach space \(^*X\) satisfying \(( ^*X )^ *= X\). In this paper, we introduce X-valued Bourgain–Morrey spaces. We show that \(^*X\)-valued block spaces are the predual of X-valued Bourgain–Morrey spaces. We obtain the completeness, denseness, and Fatou property of \(^*X\)-valued block spaces. We give a description of the dual of X-valued Bourgain–Morrey spaces and conclude the reflexivity of these spaces. The boundedness of powered Hardy–Littlewood maximal operator in vector-valued block spaces is obtained.

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Banach空间的前似值Bourgain-Morrey空间

设X是一个巴拿赫空间，使得存在一个巴拿赫空间\(^*X\)满足\(( ^*X )^ *= X\)。本文引入了x值Bourgain-Morrey空间。我们证明了\(^*X\)值块空间是x值Bourgain-Morrey空间的前双元。得到了\(^*X\) -值块空间的完备性、密集性和法头性质。给出了x值bourgin - morrey空间对偶的描述，并得出了这些空间的自反性。得到了幂Hardy-Littlewood极大算子在向量值块空间中的有界性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annals of Functional Analysis MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.00

自引率

10.00%

发文量

期刊介绍： Annals of Functional Analysis is published by Birkhäuser on behalf of the Tusi Mathematical Research Group. Ann. Funct. Anal. is a peer-reviewed electronic journal publishing papers of high standards with deep results, new ideas, profound impact, and significant implications in all areas of functional analysis and all modern related topics (e.g., operator theory). Ann. Funct. Anal. normally publishes original research papers numbering 18 or fewer pages in the journal’s style. Longer papers may be submitted to the Banach Journal of Mathematical Analysis or Advances in Operator Theory. Ann. Funct. Anal. presents the best paper award yearly. The award in the year n is given to the best paper published in the years n-1 and n-2. The referee committee consists of selected editors of the journal.