On a two-weighted estimation of maximal operator in the Lebesgue space with variable exponent - Mamedov, Farman I.; Zeren, Yusuf (SPRINGER HEIDELBERG, 2011)
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.
Keywords: Maximal functions; Weighted Lebesgue spaces; Variable exponent; Two-weight inequality; NORM INEQUALITIES; REGULARITY; Mathematics