Weighted Sobolev inequalities of mixed norm
type: Item
instance of: scholarly article
title: Weighted Sobolev inequalities of mixed norm
zbMATH Open document ID: 0879.46009
author: Seng-Kee Chua
published in: Real Analysis Exchange
publication date: 1997-12-10T00:00:00Z
review text: Let \(1<p\leq q<\infty \), let \(R=I\times J\) be a parallelepiped, and let \(v,w\) be weights. \textit{X. Shi} and \textit{A. Torchinsky} [Proc. Am. Math. Soc. 118, No. 4, 1117-1124 (1993; Zbl 0779.42011)] gave a sufficient condition on \(v, w\) in order that the Poincaré inequality \[ w(R)^{-1/q}|f-f_R|_{q(w)}\leq C|I|^{1/n}v(R)^{-1/p}|\nabla_1f|_{p(v)}+ C|J|^{1/m}v(R)^{-1/p}|\nabla_2f|_{p(v)} \] holds. The author generalizes this result to mixed norm inequalities on parallelepipeds and also to inequalities on products of domains satisfying the Boman chain condition (recall that this class contains for example Lipschitz domains).
reviewed by: Luboš Pick
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 26D10
zbMATH DE Number: 1095847
zbMATH Keywords: weighted Poincaré inequality
zbMATH Keywords: mixed norm
zbMATH Keywords: \(A_ p\)-weights
zbMATH Keywords: Boman chain condition
zbMATH Keywords: Lipschitz domain
MaRDI profile type: Publication
Recommended article: Weighted Sobolev inequality in grand mixed norm Lebesgue spaces
Recommended article: Weighted Sobolev inequality
Recommended article: The weighted Sobolev and mean value inequalities
Recommended article: Weighted Norm Estimates for Sobolev Spaces
Recommended article: Q3414487
Recommended article: Q3728633
Recommended article: Weighted norm inequalities in mixed homogeneity spaces
Recommended article: Weighted Hardy's inequalities with mixed norms
Recommended article: Weighted Sobolev-Lieb-Thirring inequalities
Recommended article: On weighted Hardy inequalities in mixed norms
description: scientific article; zbMATH DE number 1095847