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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

ABSTRACT

We give the boundedness of the Hardy-Littlewood maximal operator M λ , λ 1 , on central Herz-Morrey-Musielak-Orlicz spaces H Φ , q , ω ( X ) over bounded non-doubling metric measure spaces and to establish a generalization of Sobolev's inequality for Riesz potentials I α , τ f , τ 1 , α > 0 , of functions in such spaces. As an application and example, we obtain the boundedness of M λ and I α , τ for double phase functionals Φ such that Φ ( x , t ) = t p ( x ) + a ( x ) t q ( x ) ,   x X ,   t 0 . 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 中号 λ λ 1个 ,位于Herz-Morrey-Musielak-Orlicz中央空间 H Φ q ω X 超越有界非加倍度量空间并建立Sobolev对Riesz势不等式的推广 一世 α τ F τ 1个 α > 0 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 中号 λ 一世 α τ 用于双相功能Φ Φ X Ť = Ť p X + 一种 X Ť q X   X X   Ť 0 。这些结果是新的,即使对于度量标准度量设置加倍。

更新日期:2021-01-08
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