Two-weight norm estimates for maximal and Calderón–Zygmund operators in variable exponent Lebesgue spaces

Abstract

Two-weight norm estimates for Hardy-type transforms, maximal functions and singular integrals in variable exponent Lebesgue spaces defined, generally speaking, on spaces of homogeneous type (quasi-metric measure spaces with doubling measure) are established. The derived conditions are written in terms of norms and are simultaneously necessary and sufficient for appropriate inequalities mainly in the case when weights are of radial type. An appropriate example of a pair of non-Muckenhoupt weights governing the two-weight estimate for maximal and Calderón–Zygmund operators is also constructed.