Abstract
We study two-weight inequalities with general-type weights for Hardy-Littlewood maximal operator in the Lebesgue spaces with variable exponent. The exponent function satisfies log-Holder-type local continuity condition and decay condition in infinity. The right-hand side weight to the certain power satisfies the doubling condition. Sawyer-type two-weight criteria for fractional maximal functions are derived.
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Mamedov, F.I., Zeren, Y. On a two-weighted estimation of maximal operator in the Lebesgue space with variable exponent. Annali di Matematica 190, 263–275 (2011). https://doi.org/10.1007/s10231-010-0149-y
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DOI: https://doi.org/10.1007/s10231-010-0149-y