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On Embeddings of Logarithmic Bessel Potential Spaces

✍ Scribed by David E. Edmunds; Petr Gurka; Bohumı́r Opic

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
471 KB
Volume
146
Category
Article
ISSN
0022-1236

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✦ Synopsis

We present embedding theorems for certain logarithmic Bessel potential spaces modelled upon generalized Lorentz Zygmund spaces and clarify the role of the logarithmic terms involved in the norms of the space mentioned. In particular, we get refinements of the Sobolev embedding theorems, Trudinger's limiting embedding as well as embeddings of Sobolev spaces into space of *-Ho lder-continuous functions including the result of Bre zis and Wainger.

1997 Academic Press

1. Introduction

Classical Sobolev spaces, based upon the Lebesgue spaces L p , have played a significant role in numerous parts of mathematics for many years. However, it has gradually become clear that there are considerable advantages to be gained by using as a base a scale of spaces which can be more finely tuned than the Lebesgue scale. For example, replacement of the L p spaces by the spaces L p (log L) q of Zygmund type has been used by Edmunds and Triebel [10] to obtain estimates of the eigenvalues of degenerate elliptic differential operators with coefficients having singular behaviour. The same article no. FU963037

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