Spectral synthesis in weighted Sobolev spaces
type: Item
instance of: scholarly article
title: Spectral synthesis in weighted Sobolev spaces
zbMATH Open document ID: 0911.46021
author: N. O. Belova
published in: Siberian Advances in Mathematics
publication date: 1999-02-24T00:00:00Z
review text: The author generalizes Hedberg's results on spectral synthesis in Sobolev spaces to the case of weighted Sobolev spaces whose weights satisfy the Muckenhoupt condition. The density of the set of compactly supported smooth functions is proved using techniques of weighted nonlinear potential theory and embeddings theorems. The \(L_q\) approximation by solutions of elliptic equations is also considered and necessary and sufficient conditions are given for the stability in weighted Sobolev spaces. The results have been announced in [Math. Notes 56, No. 2, 856-858 (1994); translation from Mat. Zametki 56, No. 2, 136-139 (1994; Zbl 0851.46025)].
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 43A45
zbMATH DE Number: 1047522
zbMATH Keywords: weighted Sobolev spaces
zbMATH Keywords: Muckenhoupt condition
zbMATH Keywords: weighted Poincaré inequality
zbMATH Keywords: capacity
zbMATH Keywords: approximation problems
zbMATH Keywords: stability in Sobolev spaces
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1047522