Editor's note: the differentiability of functions in \({\mathbb{R}}^ n\)
type: Item
instance of: scholarly article
title: Editor's note: the differentiability of functions in \({\mathbb{R}}^ n\)
zbMATH Open document ID: 0531.46021
published in: Annals of Mathematics. Second Series
publication date: 1981-01-01T00:00:00Z
review text: The following theorem is proven: suppose \(F:{\mathbb{R}}^ n\to {\mathbb{R}}\) be such that \(\nabla F\in L^{n,1}_{loc}\) in the distribution sense \((L^{n,1}\) being a Lorentz space). Then F is equivalent to a continuous function and differentiable a.e. The proof is based on a suitable new maximal inequality proven as a lemma.
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 26B05
Mathematics Subject Classification ID: 42B25
zbMATH DE Number: 3842495
zbMATH Keywords: Lorentz space
zbMATH Keywords: maximal inequality
reviewed by: Srishti D. Chatterji
MaRDI profile type: Publication
author: Elias M. Stein
description: scientific article; zbMATH DE number 3842495