Journal of Inequalities and Applications
Volume 7 (2002), Issue 5, Pages 747-758
doi:10.1155/S1025583402000383
A note on Ap weights: Pasting weights and changing variables
Departamento de Matemtáicas, Universidad de Zaragoza, Zaragoza 50009, Spain
Received 29 June 2001; Revised 12 September 2001
Copyright © 2002 Mario Pérez Riera. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
For two weights u, w on ℝn, we show that w∈Ap,u (the Muckenhoupt class of weights) if and only if wu∈Ap and wu1−p∈Ap, under the assumption that u∈Ar for every r>1. We also prove a rather general result on pasting weights on ℝ that satisfy the Ap condition.