Analysis reveals boundedness of fractional integral operators in metric measure spaces, indicating Sobolev-type inequalities may apply for multiphase functions.
In this paper, we discuss the boundedness of generalized fractional integral operators on Musielak–Orlicz–Morrey spaces of an integral form over bounded non‐doubling metric measure spaces , where both and depend on . As an application, we give Sobolev‐type inequalities for multiphase functions where , , and are log‐Hölder continuous, for , and and are nonnegative, bounded, and Hölder continuous.
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Ohno et al. (2025) studied this question.
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