What question did this study set out to answer?

The aim is to analyze the boundedness of the commutator associated with the rough fractional maximal operator on variable exponent central Morrey spaces.

February 2, 2026Open Access

Boundedness of Commutators Generated by the Rough Fractional Maximal Operator on Variable Exponent Central Morrey Spaces

Key Points

The aim is to analyze the boundedness of the commutator associated with the rough fractional maximal operator on variable exponent central Morrey spaces.
Utilized spherical harmonic decomposition of kernels.
Applied sharp maximal function estimates.
Employed variable exponent space theory.
Established conditions under which the boundedness holds.
Demonstrated that suitable regularity on variable exponents is crucial.

Abstract

In this paper, using harmonic analysis tools−including spherical harmonic decomposition of kernels, sharp maximal function estimates, and variable exponent space theory—we investigate the boundedness of the commutator b,MΩ,β on variable exponent central Morrey spaces, under suitable regularity conditions on the variable exponents. Here, Ω∈Ll(Sn−1) (l≥1) denotes a zero-degree homogeneous function on the unit sphere Sn−1, β satisfies 0≤β<n, and b∈CBMO(Rn).

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Cite This Study

Yang et al. (Fri,) studied this question.

synapsesocial.com/papers/6980fe00c1c9540dea80fc2e https://doi.org/https://doi.org/10.3390/axioms15020100

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