Global subrepresentation formulas in chain domains with irregular boundaries. (October 2022)

• Record Type: Journal Article
• Authors: Chua, Seng-Kee; Wheeden, Richard L.
• Is Part Of: Nonlinear analysis. Volume 223(2022)
• Publication Date: 2022-10
• Subjects: primary 46E35 26D10; Φ-John domains -- Power weights -- Poincare type inequality -- Quasi-metric -- John domains -- Doubling and weak doubling weights; 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.2022.112998
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: For a large class of chain domains with rough boundaries, we derive global subrepresentation formulas (i.e., pointwise inequalities reminiscent of part of the Fundamental Theorem of Calculus). The results are new even for John and Boman domains. We also show how they lead to global first order Poincaré–Sobolev estimates in a large collection of Φ -John domains. The restriction on Φ is expressed as an integral condition on the number of chaining balls of various specific sizes.