Parametric Marcinkiewicz Integral and Its Higher-Order Commutators on Variable Exponents Morrey-Herz Spaces

We focus on two-phase problems with singular and superlinear parametric terms on the right-hand side. Using fibering maps and the Nehari manifold method, we prove that there are at least two non-trivial positive solutions in a geometric setting that is locally similar to Euclidean spaces but has different global properties for all except the smallest values of parameter $$\mu > 0.$$ μ > 0 . Singularities may appear at discrete locations in the manifold, which is a challenge for the work due to the unpredictable behavior of the solution. The findings presented here generalize some known results.

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Parametric Marcinkiewicz Integral and Its Higher-Order Commutators on Variable Exponents Morrey-Herz Spaces

Abstract: In this article, we prove the boundedness of the parametric Marcinkiewicz integral and its higher-order commutators generated by BMO spaces on the variable Morrey-Herz space. All the results are new even when α · is a constant.

Cited by 4 publications

References 48 publications

Parametrized Marcinkiewicz Integrals on Herz Spaces with Variable Exponents

Parametrized Marcinkiewicz Integrals on Herz Spaces with Variable Exponents

Fractional type Marcinkiewicz integral and its commutator on grand variable Herz-Morrey spaces

Singular two-phase problem on a complete manifold: analysis and insights

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