On sharp embeddings of Besov and Triebel-Lizorkin spaces in the subcritical case
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Abstract:
We discuss the growth envelopes of Fourier-analytically defined Besov and Triebel-Lizorkin spaces $B^s_{p,q}(\mathbb {R}^n)$ and $F^s_{p,q} (\mathbb {R}^n)$ in the limiting case $s=\sigma _p:=n\max (\frac 1p-1,0)$. These results may also be reformulated as optimal embeddings into the scale of Lorentz spaces $L_{p,q}(\mathbb {R}^n)$. We close several open problems outlined already in [H. Triebel, The structure of functions, Birkhäuser, Basel, 2001] and explicitly stated in [D. D. Haroske, Envelopes and sharp embeddings of function spaces, Chapman & Hall/CRC, Boca Raton, FL, 2007].References
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Additional Information
- Jan Vybíral
- Affiliation: Mathematisches Institut, Universität Jena, Ernst-Abbe-Platz 2, 07740 Jena, Germany
- Email: vybiral@mathematik.uni-jena.de
- Received by editor(s): July 14, 2008
- Published electronically: September 2, 2009
- Communicated by: Andreas Seeger
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 141-146
- MSC (2000): Primary 46E35, 46E30
- DOI: https://doi.org/10.1090/S0002-9939-09-09832-3
- MathSciNet review: 2550178