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Sobolev's inequality in central Herz-Morrey-Musielak-Orlicz spaces over metric measure spaces
Complex Variables and Elliptic Equations ( IF 0.6 ) Pub Date : 2021-01-08 Takao Ohno, Tetsu Shimomura
中文翻译:
度量度量空间上中心Herz-Morrey-Musielak-Orlicz空间中的Sobolev不等式
更新日期:2021-01-08
Complex Variables and Elliptic Equations ( IF 0.6 ) Pub Date : 2021-01-08 Takao Ohno, Tetsu Shimomura
ABSTRACT
We give the boundedness of the Hardy-Littlewood maximal operator , , on central Herz-Morrey-Musielak-Orlicz spaces over bounded non-doubling metric measure spaces and to establish a generalization of Sobolev's inequality for Riesz potentials , , , of functions in such spaces. As an application and example, we obtain the boundedness of and for double phase functionals Φ such that . These results are new even for the doubling metric measure setting.
中文翻译:
度量度量空间上中心Herz-Morrey-Musielak-Orlicz空间中的Sobolev不等式
摘要
我们给出了Hardy-Littlewood极大算子的有界性 , ,位于Herz-Morrey-Musielak-Orlicz中央空间 超越有界非加倍度量空间并建立Sobolev对Riesz势不等式的推广 , , 在这种空间中的功能。作为一个应用程序和示例,我们获得了 和 用于双相功能Φ 。这些结果是新的,即使对于度量标准度量设置加倍。