Characterization of boundedness of some commutators of fractional maximal functions in terms of $p$-adic vector spaces

J. Wu; Y. Chang

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arXiv · 2308.02736

Characterization of boundedness of some commutators of fractional maximal functions in terms of $p$-adic vector spaces

J. Wu·Y. Chang

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Abstract

This paper gives some characterizations of the boundedness of the maximal or nonlinear commutator of the $p$-adic fractional maximal operator $ \mathcal{M}_{\alpha}^{p}$ with the symbols belong to the $p$-adic BMO spaces on (variable) Lebesgue spaces and Morrey spaces over $p$-adic field, by which some new characterizations of BMO functions are obtained in the $p$-adic field context. Meanwhile, Some equivalent relations between the $p$-adic BMO norm and the $p$-adic (variable) Lebesgue or Morrey norm are given.

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BibTeX RIS

J. Wu, Y. Chang. 2023-08-04. Characterization of boundedness of some commutators of fractional maximal functions in terms of $p$-adic vector spaces. https://arxiv.org/abs/2308.02736

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