Critical imbeddings with multivariate rearrangements

by    M. Krbec, H.-J. Schmeisser

Preprint series: 06-15, Analysis

The paper is published: Jenaer Schriften zur Mathematik und Informatik, Math/Inf/04/06, Universität Jena, Germany, 2006.

46E35 Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
42B35 Function spaces arising in harmonic analysis

Abstract: Our concern in this paper lies with imbeddings of general spaces of Besov and Lizorkin-Triebel type with dominating mixed derivatives in the rst critical case. We employ multivariate exponential Orlicz and Lorentz-Orlicz spaces in the role of targets. We study basic properties of the target spaces, in particular, we compare them with usual ex- ponential spaces, showing that in this case the multivariate clones are in fact better adapted to the character of smoothness of the imbed- ded spaces. Then we prove sharp limiting imbedding theorems and establish estimates for the multivariate growth envelope functions.

Keywords: Sobolev spaces, Bessel potential spaces, Besov spaces, Lizorkin- Triebel spaces, exponential Orlicz spaces, Lorentz-Zygmund spaces, limiting imbeddings, dominating mixed derivatives.

Upload: 2006-11-16

Update: 2006 -11 -16

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