度量测度空间上的Morrey空间和Campanato空间理论

摘要

The classical Morrey spaces and Campanato spaces, which play an important role in researches of regularities of partial differential equations, are defined on open sets of the Euclidean spaces with the Lebesgue measures. In this paper, we define Morrey spaces and Campanato spaces on metric measure spaces, and discuss some properties of them, which generalize the classical theories on Morrey spaces and Campanato spaces.%经典的Morrey空间和Campanato空间的理论是在欧氏空间的开集上、运用Lebesgue测度定义的,这些理论在偏微分方程的正则性研究中发挥着非常重要的作用.本文在度量测度空间上定义了Morrey空间和Campanato空间,并讨论了它们的一些性质,推广了经典的Morrey空间和Campanato空间理论.