On the extension of Muckenhoupt weights in metric spaces. (February 2022)

• Record Type: Journal Article
• Authors: Kurki, Emma-Karoliina; Mudarra, Carlos
• Is Part Of: Nonlinear analysis. Volume 215(2022)
• Publication Date: 2022-02
• Subjects: 30L99 -- 42B25 -- 42B37; Muckenhoupt weight -- Metric measure space -- Doubling condition; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2021.112671
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: A theorem by Wolff states that weights defined on a measurable subset of R n and satisfying a Muckenhoupt-type condition can be extended into the whole space as Muckenhoupt weights of the same class. We give a complete and self-contained proof of this theorem generalized into metric measure spaces supporting a doubling measure. Related to the extension problem, we also show estimates for Muckenhoupt weights on Whitney chains in the metric setting.