Lipschitz-Type Estimates for Commutators of Rough Fractional Maximal Operators with Variable Kernels on Variable Exponent Lebesgue Spaces
Chapter from the book:
Gürbüz,
F.
(ed.)
2025.
Open Problems in Mathematics and Science.
Synopsis
In this work, we investigate the boundedness properties of commutators generated by rough fractional maximal operators with variable kernels on variable exponent Lebesgue spaces. By combining techniques from harmonic analysis with modular inequalities associated with variable exponent function spaces, we obtain Lipschitz-type estimates for these commutators under suitable assumptions on the kernels and the variable exponents. Our results extend and improve several known boundedness results in both classical and variable exponent Lebesgue spaces. In particular, we demonstrate how the interaction between variable kernels, fractional behavior, and nonstandard growth conditions influences the continuity of these commutators.
