Abstract
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.
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