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Journal of Function Spaces and Applications
Volume 7 (2009), Issue 3, Pages 251-288

Spaces of Sobolev type with positive smoothness on ℝn, embeddings and growth envelopes

Cornelia Schneider, Universität Leipzig, PF 100920, D-04009 Leipzig, Germany

Received 1 June 2008

Academic Editor: Hans Triebel

Copyright © 2009 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We characterize Triebel-Lizorkin spaces with positive smoothness on n, obtained by different approaches. First we present three settings Fp,qs(n),Fp,qs(n),p,qs(n) associated to definitions by differences, Fourier-analytical methods and subatomic decompositions. We study their connections and diversity, as well as embeddings between these spaces and into Lorentz spaces. Secondly, relying on previous results obtained for Besov spaces 𝔅p,qs(n), we determine their growth envelopes 𝔈G(Fp,qs(n)) for 0p, 0q, s0, and finally discuss some applications.