Abstract
We study a characterization of the precompactness of sets in variable exponent Morrey spaces on bounded metric measure spaces. Totally bounded sets are characterized from several points of view for the case of variable exponent Morrey spaces over metric measure spaces. This characterization is new in the case of constant exponents.
Highlights
We investigate relatively compact sets in variable exponent Morrey spaces
The aim of the paper is to characterize precompact sets in variable exponent Morrey spaces on an arbitrary doubling metric measure space
We refer to [3,10,11] for the characterization of precompact sets in variable exponent Lebesgue spaces on an arbitrary doubling metric measure space
Summary
We investigate relatively compact sets in variable exponent Morrey spaces. The aim of the paper is to characterize precompact sets in variable exponent Morrey spaces on an arbitrary doubling metric measure space. We refer to [3,10,11] for the characterization of precompact sets in variable exponent Lebesgue spaces on an arbitrary doubling metric measure space. There are various advances in the study of variable exponent Morrey function spaces [2,15,16,25] Those types of spaces have emerged very recently (we refer the reader to [26,28] to see the classical setting). A characterization of relatively compact sets in variable exponent Morrey spaces over metric measure spaces is proved in Sect. We present some examples, remarks, and an open problem
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