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[Untitled]
- Source :
- Analysis Mathematica. 26:299-319
- Publication Year :
- 2000
- Publisher :
- Springer Science and Business Media LLC, 2000.
-
Abstract
- In a recent paper Edmunds, Gurka, and Opic [5] showed that Sobolev spaces of order k, based on the Zygmund spaces L n/k (log L)α (R n ), are continuously embedded into L ∞ (R n ) if α > 1/p′, p n/k. In this paper we replace L n/k (log L)α (R n ) by the Lebesgue space L n/k (R n ) and increase the smoothness of the functions involved by a "logarithmic" order α > 1/p′ to obtain the continuous embedding into L ∞ (R n ). Both approaches turn out to be equivalent. We also derive results of Trudinger-type [16] on embeddings into Orlicz spaces in the limit case k = n/p as well as results of Brezis-Wainger-type [2] on almost Lipschitz continuity in the superlimiting case k = n/p + 1.
Details
- ISSN :
- 01333852
- Volume :
- 26
- Database :
- OpenAIRE
- Journal :
- Analysis Mathematica
- Accession number :
- edsair.doi...........659c24014edec3789dde4116f3b64167