Muckenhoupt weights

Abstract

This chapter aims at developing a certain feeling for Muckenhoupt weights. Power weights are a simple class of Muckenhoupt weights, but we have a long way to go in finding a sufficient supply of nontrivial Muckenhoupt weights. We have in particular to prove the so-called reverse Milder inequality, which implies that if w is a weight in A p (Γ) then ω1+ε belongs to A p (Γ) for all sufficiently small ∣ε∣(“stability” of Muckenhoupt weights). For weights with only one singularity, we establish a criterion for their membership in A p (Γ) in terms of the W transform. It is this criterion which will enable us to identify plenty of oscillating weights as Muckenhoupt weights.KeywordsMaximal OperatorMeasurable SubsetPeriodic ReproductionPower WeightSublinear OperatorThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.