Two-weighted inequalities for maximal operator in generalized weighted Morrey spaces on spaces of homogeneous type

Abstract

In this paper we give a characterization of two-weighted inequalities for maximal operators in generalized weighted Morrey spaces on spaces of homogeneous type Mp,φω (X). We prove the boundedness of maximal operator M from the spaces Mp,φ1ωδ 1(X)to the spaces Mp,φ2ωδ2(X), where 1 < p < ∞, 0 < δ < 1 and (ω1, ω2) ∈ Aep(X).