Traces of weighted Sobolev spaces with Muckenhoupt weight. The case p=1. (November 2015)

• Record Type: Journal Article
• Authors: Tyulenev, A.I.
• Is Part Of: Nonlinear analysis. Volume 128(2015)
• Page Start: 248
• Page End: 272
• Publication Date: 2015-11
• Subjects: 46E35; Besov spaces of variables smoothness -- Weighted Sobolev spaces -- Traces -- Muckenhoupt 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.2015.08.001
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: A complete description of traces on R n of functions from the weighted Sobolev space W 1 l ( R n + 1, γ ), l ∈ N, with weight γ ∈ A 1 loc ( R n + 1 ) is obtained. In the case l = 1 the proof of the trace theorem is based on a special nonlinear algorithm for constructing a system of tilings of the space R n . As the trace of the space W 1 1 ( R n + 1, γ ) we have the new function space Z ( { γ k, m } ) .