In this paper, the main aim is to give some characterizations of the boundedness of the maximal or nonlinear commutator of the -adic fractional maximal operator with the symbols belong to the -adic Lipschitz spaces in the context of the -adic version of variable Lebesgue spaces, by which some new characterizations of the Lipschitz spaces and nonnegative Lipschitz functions are obtained in the -adic field context. Meanwhile, Some equivalent relations between the -adic Lipschitz norm and the -adic variable Lebesgue norm are also given.
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Keywords: $p$-adic field, Lipschitz function, fractional maximal function, variable exponent Lebesgue space
Jianglong Wu 1; Yunpeng Chang 1
CC-BY 4.0
@article{CRMATH_2024__362_G2_177_0,
author = {Jianglong Wu and Yunpeng Chang},
title = {Characterization of {Lipschitz} {Spaces} via {Commutators} of {Fractional} {Maximal} {Function} on the $p${-Adic} {Variable} {Exponent} {Lebesgue} {Spaces}},
journal = {Comptes Rendus. Math\'ematique},
pages = {177--194},
publisher = {Acad\'emie des sciences, Paris},
volume = {362},
year = {2024},
doi = {10.5802/crmath.563},
language = {en},
}
TY - JOUR AU - Jianglong Wu AU - Yunpeng Chang TI - Characterization of Lipschitz Spaces via Commutators of Fractional Maximal Function on the $p$-Adic Variable Exponent Lebesgue Spaces JO - Comptes Rendus. Mathématique PY - 2024 SP - 177 EP - 194 VL - 362 PB - Académie des sciences, Paris DO - 10.5802/crmath.563 LA - en ID - CRMATH_2024__362_G2_177_0 ER -
%0 Journal Article %A Jianglong Wu %A Yunpeng Chang %T Characterization of Lipschitz Spaces via Commutators of Fractional Maximal Function on the $p$-Adic Variable Exponent Lebesgue Spaces %J Comptes Rendus. Mathématique %D 2024 %P 177-194 %V 362 %I Académie des sciences, Paris %R 10.5802/crmath.563 %G en %F CRMATH_2024__362_G2_177_0
Jianglong Wu; Yunpeng Chang. Characterization of Lipschitz Spaces via Commutators of Fractional Maximal Function on the $p$-Adic Variable Exponent Lebesgue Spaces. Comptes Rendus. Mathématique, Volume 362 (2024), pp. 177-194. doi : 10.5802/crmath.563. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.563/
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