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arXiv · 2511.08118

On the mixed Bourgain-Morrey spaces

Tengfei Bai·Pengfei Guo·Jingshi Xu
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Abstract

We introduce the mixed Bourgain-Morrey spaces and obtain their preduals. The boundedness of Hardy-Littlewood maximal operator, iterated maximal operator, fractional integral operator, singular integral operator on these spaces is proved. The Littlewood-Paley theory for mixed Bourgain-Morrey spaces and their preduals are established. As applications, we consider wavelet characterizations for mixed Bourgain-Morrey spaces and a fractional chain rule in mixed Bourgain-Morrey Triebel-Lizorkin spaces. In addition, we give a description of the dual of mixed Bourgain-Morrey spaces and conclude the reflexivity of these spaces.

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Tengfei Bai, Pengfei Guo, Jingshi Xu. 2025-11-11. On the mixed Bourgain-Morrey spaces. https://arxiv.org/abs/2511.08118

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