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arXiv · 2406.11531

Precompactness in matrix weighted Bourgain-Morrey spaces

Tengfei Bai·Jingshi Xu
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Abstract

In this paper, we introduce matrix weighted Bourgain-Morrey spaces and obtain two sufficient conditions for precompact sets in matrix weighted Bourgain-Morrey spaces. We prove that the dyadic average operator is bounded on some matrix weighted Bourgain-Morrey spaces. With this result, we obtain the necessity for precompact sets in some matrix weighted Bourgain-Morrey spaces. The results are new even for the unweighted Bourgain-Morrey spaces.

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Tengfei Bai, Jingshi Xu. 2024-06-17. Precompactness in matrix weighted Bourgain-Morrey spaces. https://doi.org/10.2298/fil2518261b

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