The structure of increasing weights on the real line

Abstract

We examine the structure of a variety of related weight classes on the real line and the positive real axis: doubling measures, Ap weights, the Bp weights of Ari˜no and Muckenhoupt, and 2 Young functions. We give a number of characterizations of these classes. As applications we compute the Matuszewska- Orlicz indices of a Young function due to Lindberg [27], give a sufficient condition for a function m to be a multiplier of the doubling measures on R+ and answer a question on quasi-symmetric mappings raised by the first author in [4].