矩阵加权Bourgain-Morrey空间中的预紧性
Precompactness in matrix weighted Bourgain-Morrey spaces
AI总结：
本文研究了矩阵加权Bourgain-Morrey空间中预紧集的条件，证明了二进制平均算子的有界性，并揭示了预紧集的必要性。
摘要：
本文引入了矩阵加权Bourgain-Morrey空间，并获得了矩阵加权Bourgain-Morrey空间中预紧集的两个充分条件。我们证明了二进制平均算子在某些矩阵加权Bourgain-Morrey空间上是有界的。借助这一结果，我们获得了某些矩阵加权Bourgain-Morrey空间中预紧集的必要性。这些结果即使在无权重Bourgain-Morrey空间中也是新的。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
