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arXiv · 2106.04926

Necessary and sufficient conditions for boundedness of commutators of fractional integral operators on mixed-norm Lebesgue spaces

Houkun Zhang·Jiang Zhou
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Abstract

In this paper, the sharp maximal theorem is generalized to mixed-norm ball Banach function spaces, which is defined as Definition 2.7. As an application, we give a characterization of BMO via the boundedness of commutators of fractional integral operators on mixed-norm Lebesgue spaces. Moreover, the characterization of homogeneous Lipschitz space is also given by the boundedness of commutators of fractional integral operators on mixed-norm Lebesgue spaces. Finally, two applications of Corollary 6.4 are given.

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Houkun Zhang, Jiang Zhou. 2021-06-09. Necessary and sufficient conditions for boundedness of commutators of fractional integral operators on mixed-norm Lebesgue spaces. https://arxiv.org/abs/2106.04926

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