Generalized Rademacher-Stepanov type theorem and applications
type: Item
instance of: scholarly article
title: Generalized Rademacher-Stepanov type theorem and applications
zbMATH Open document ID: 1180.58007
DOI: 10.4171/ZAA/1384
author: Alireza Ranjbar-Motlagh
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 2009-10-15T00:00:00Z
review text: The author generalizes a theorem of Stepanov which provides a necessary and sufficient condition for almost everywhere differentiability of functions over Euclidean spaces. Precisely, an \(L^p\)-type generalization of the Stepanov theorem is proved and it is extended to the settings of Orlicz spaces. An application of this generalized Rademacher-Stepanov type theorem is given to the Sobolev and bounded variation maps with values into a metric space. It is shown that several generalized differentiability type theorems are valid for Sobolev maps acting from a Lipschitz manifold into a metric space. As a byproduct, it is shown that the Sobolev spaces of Korevaar-Schoen and Reshetnyak are equivalent.
Mathematics Subject Classification ID: 58C20
Mathematics Subject Classification ID: 46E30
zbMATH DE Number: 5615424
zbMATH Keywords: Rademacher and Stepanov theorems
zbMATH Keywords: Sobolev and bounded variation spaces
zbMATH Keywords: generalized differentiability
zbMATH Keywords: Lipschitz manifolds
zbMATH Keywords: Orlicz spaces
reviewed by: Dian K. Palagachev
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5615424