Journal of Function Spaces

Journal of Function Spaces / 2009 / Article

Open Access

Volume 7 |Article ID 815676 |

Cornelia Schneider, "Spaces of Sobolev type with positive smoothness on ℝn, embeddings and growth envelopes", Journal of Function Spaces, vol. 7, Article ID 815676, 38 pages, 2009.

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

Academic Editor: Hans Triebel
Received01 Jun 2008


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.

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.

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