Ap Weights in Directionally (γ,m) Limited Space and Applications

Abstract

Let (X,d) be a directionally (γ,m)-limited space with every γ ∈(0,∞). In this setting, we aim to study an analogue of the classical theory of Ap(μ) weights. As an application, we establish some weighted estimates for the Hardy–Littlewood maximal operator. Then, we introduce the relationship between directionally (γ,m)-limited spaceand geometric doubling. Finally, we obtain the weighted norm inequalities of the Calderón–Zygmund operator and commutator in non-homogeneous space.