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<p>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 <i>Q</i>-regular measures. As an application, we study Sobolev inequalities for double phase functionals with variable exponents.</p>

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Sobolev Inequalities in Non-homogeneous Central Musielak–Orlicz–Morrey Spaces over Metric Measure Spaces and Double Phase Functionals

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月9日

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  • Takao Ohno,
  • Tetsu Shimomura

摘要

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.