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arXiv · 2505.19143

The preduals of Banach space valued Bourgain-Morrey spaces

Tengfei Bai·Pengfei Guo·Jingshi Xu
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Abstract

Let $X$ be a Banach space such that there exists a Banach space $^\ast X$ and $ ( ^\ast X )^ \ast = X $. In this paper, we introduce $X$-valued Bourgain-Morrey spaces. We show that $^\ast X$-valued block spaces are the predual of $X$-valued Bourgain-Morrey spaces. We obtain the completeness, denseness and Fatou property of $^\ast X$-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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Tengfei Bai, Pengfei Guo, Jingshi Xu. 2025-05-25. The preduals of Banach space valued Bourgain-Morrey spaces. https://doi.org/10.1007/s43034-025-00458-w

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