Norms of embeddings of logarithmic Bessel potential spaces

Let \Omega be a subset of \mathbb{R}\sp{n} with finite volume, let \nu >0 and let \Phi be a Young function with \Phi (t) = \exp (\exp t\sp{\nu }) for large t. We show that the norm on the Orlicz space L\sb {\Phi } (\Omega ) is equivalent to \begin{equation*}\sup \sb {1

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 1998-08, Vol.126 (8), p.2417-2425
Main Authors: Edmunds, David E., Gurka, Petr, Opic, Bohumír
Format: Article
Language:English
Subjects:
Embeddings
Entropy
Grants
Mathematical analysis
Mathematical functions
Mathematical inequalities
Mathematical theorems
Orlicz space
Research grants
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Summary:Let \Omega be a subset of \mathbb{R}\sp{n} with finite volume, let \nu >0 and let \Phi be a Young function with \Phi (t) = \exp (\exp t\sp{\nu }) for large t. We show that the norm on the Orlicz space L\sb {\Phi } (\Omega ) is equivalent to \begin{equation*}\sup \sb {1
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-98-04327-5