On sharp condition for imbedding anisotropic Sobolev-Orlicz spaces in a space of continuous functions
type: Item
instance of: scholarly article
title: On sharp condition for imbedding anisotropic Sobolev-Orlicz spaces in a space of continuous functions
zbMATH Open document ID: 0799.46044
DOI: 10.1007/BF01236779
author: E. A. Rozenfel'd
published in: Mathematical Notes
publication date: 1993-04-01T00:00:00Z
review text: Let \(G\subset R^ n\) be a open and bounded set and \(f = (f_ 1, \dots, f_ n)\), where \(f_ i : [0, \infty) \to [0, \infty]\) is Young's function for \(i=1, \dots,n\). The author establishes necessary and sufficient conditions for imbedding anisotropic Sobolev-Orlicz space \({\overset \circ W}^ 1_ f (G)\) into the space of continuous and bounded functions. These results are the proceeding of the author's paper studying the imbedding of isotropic Sobolev-Orlicz spaces from [Mat. Zametki, 9, No. 6, 639-650 (1971; Zbl 0219.46028)].
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 46E30
zbMATH DE Number: 148639
zbMATH Keywords: Young's function
zbMATH Keywords: anisotropic Sobolev-Orlicz space
zbMATH Keywords: isotropic Sobolev- Orlicz spaces
reviewed by: Vladimír Ďurikovič
MaRDI profile type: Publication
cites work: Fractional Integration in Orlicz Spaces. I
cites work: Q5665024
cites work: Q3218622
full work available at URL: https://doi.org/10.1007/bf01236779
OpenAlex ID: W2004030750
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description: scientific article; zbMATH DE number 148639