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1Mathematisches Institut, Universität Jena, Ernst-Abbe-Platz 2, 07737 Jena, Germany. E-mail: markus.hansen2@uni-jena.de
2Mathematisches Institut, Universität Jena, Ernst-Abbe-Platz 2, 07737 Jena, Germany. E-mail: jan.vybiral@uni-jena.de
Citation Information: Georgian Mathematical Journal. Volume 16, Issue 4, Pages 667–682, ISSN (Online) 1072-9176, ISSN (Print) 1072-947X, DOI: 10.1515/GMJ.2009.667, March 2010
We give a proof of the Jawerth embedding for function spaces with dominating mixed smoothness of Besov and Triebel–Lizorkin type
where
0 < 𝑝0 < 𝑝1 ≤ ∞ and 0 < 𝑞0,𝑞1 ≤ ∞
and
with
If 𝑝1 < ∞, we prove also the Franke embedding
Our main tools are discretization by a wavelet isomorphism and multivariate rearrangements.
Key words and phrases:: Besov spaces; Triebel–Lizorkin spaces; Sobolev embedding; dominating mixed smoothness; Jawerth–Franke embedding
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