Randomized trial investigates Sobolev inequalities for functions in various spaces, indicating broader mathematical applications.
We establish Sobolev inequalities for variable Riesz potentials of functions in non-homogeneous central Musielak–Orlicz–Morrey spaces over unbounded metric measure spaces equipped with lower Ahlfors Q -regular measures. As an application, we study Sobolev inequalities for double phase functionals with variable exponents.
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Ohno et al. (2026) studied this question.
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