论文标题
组成操作员在莫雷空间和薄弱的莫雷空间上的界限
Boundedness of composition operators on Morrey spaces and weak Morrey spaces
论文作者
论文摘要
在这项研究中，我们研究了作用于莫雷空间和薄弱空间的组成操作员的界限。这项研究的主要目的是研究由莫雷空间上的差异性引起的组成算子的界限的必要条件。特别是，详细信息来自界限，即 诱导组成算子的映射的Bi-Lipschitz连续性遵循组成映射的连续性。证据的想法是确定特征函数的莫雷范围，并采用由特征函数组成的特定函数。由于特定函数属于莫雷空间，但不属于lebesgue空间， 结果揭示了一种新现象 在Lebesgue空间中未观察到。随后，我们证明了映射引起的组成算子的界限，该映射满足了对常规空间产生的一般弱型空间的适当体积估计。作为推论，提供了在弱的莫雷空间上组成操作员的界限的必要条件。
In this study, we investigate the boundedness of composition operators acting on Morrey spaces and weak Morrey spaces. The primary aim of this study is to investigate a necessary and sufficient condition on the boundedness of the composition operator induced by a diffeomorphism on Morrey spaces. In particular, detailed information is derived from the boundedness, i.e., the bi-Lipschitz continuity of the mapping that induces the composition operator follows from the continuity of the composition mapping. The idea of the proof is to determine the Morrey norm of the characteristic functions, and employ a specific function composed of a characteristic function. As the specific function belongs to Morrey spaces but not to Lebesgue spaces, the result reveals a new phenomenon not observed in Lebesgue spaces. Subsequently, we prove the boundedness of the composition operator induced by a mapping that satisfies a suitable volume estimate on general weak-type spaces generated by normed spaces. As a corollary, a necessary and sufficient condition for the boundedness of the composition operator on weak Morrey spaces is provided.
