Precompactness in matrix weighted Bourgain-Morrey spaces
Functional Analysis
2026-03-16 v2 Classical Analysis and ODEs
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.
Cite
@article{arxiv.2406.11531,
title = {Precompactness in matrix weighted Bourgain-Morrey spaces},
author = {Tengfei Bai and Jingshi Xu},
journal= {arXiv preprint arXiv:2406.11531},
year = {2026}
}
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24 pages