Traces of anisotropic Besov-Lizorkin-Triebel spaces---a complete treatment of the borderline cases

Walter Farkas; Jon Johnsen; Winfried Sickel

Mathematica Bohemica (2000)

  • Volume: 125, Issue: 1, page 1-37
  • ISSN: 0862-7959

Abstract

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Including the previously untreated borderline cases, the trace spaces (in the distributional sense) of the Besov-Lizorkin-Triebel spaces are determined for the anisotropic (or quasi-homogeneous) version of these classes. The ranges of the traces are in all cases shown to be approximation spaces, and these are shown to be different from the usual spaces precisely in the cases previously untreated. To analyse the new spaces, we carry over some real interpolation results as well as the refined Sobolev embeddings of J. Franke and B. Jawerth to the anisotropic scales.

How to cite

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Farkas, Walter, Johnsen, Jon, and Sickel, Winfried. "Traces of anisotropic Besov-Lizorkin-Triebel spaces---a complete treatment of the borderline cases." Mathematica Bohemica 125.1 (2000): 1-37. <http://eudml.org/doc/248677>.

@article{Farkas2000,
abstract = {Including the previously untreated borderline cases, the trace spaces (in the distributional sense) of the Besov-Lizorkin-Triebel spaces are determined for the anisotropic (or quasi-homogeneous) version of these classes. The ranges of the traces are in all cases shown to be approximation spaces, and these are shown to be different from the usual spaces precisely in the cases previously untreated. To analyse the new spaces, we carry over some real interpolation results as well as the refined Sobolev embeddings of J. Franke and B. Jawerth to the anisotropic scales.},
author = {Farkas, Walter, Johnsen, Jon, Sickel, Winfried},
journal = {Mathematica Bohemica},
keywords = {anisotropic Besov and Lizorkin-Triebel spaces; approximation spaces; trace operators; boundary problems; interpolation; atomic decompositions; refined Sobolev embeddings; anisotropic scales; anisotropic Besov and Lizorkin-Triebel spaces; approximation spaces; trace operators; boundary problems; interpolation; atomic decompositions; refined Sobolev embeddings; anisotropic scales},
language = {eng},
number = {1},
pages = {1-37},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Traces of anisotropic Besov-Lizorkin-Triebel spaces---a complete treatment of the borderline cases},
url = {http://eudml.org/doc/248677},
volume = {125},
year = {2000},
}

TY - JOUR
AU - Farkas, Walter
AU - Johnsen, Jon
AU - Sickel, Winfried
TI - Traces of anisotropic Besov-Lizorkin-Triebel spaces---a complete treatment of the borderline cases
JO - Mathematica Bohemica
PY - 2000
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 125
IS - 1
SP - 1
EP - 37
AB - Including the previously untreated borderline cases, the trace spaces (in the distributional sense) of the Besov-Lizorkin-Triebel spaces are determined for the anisotropic (or quasi-homogeneous) version of these classes. The ranges of the traces are in all cases shown to be approximation spaces, and these are shown to be different from the usual spaces precisely in the cases previously untreated. To analyse the new spaces, we carry over some real interpolation results as well as the refined Sobolev embeddings of J. Franke and B. Jawerth to the anisotropic scales.
LA - eng
KW - anisotropic Besov and Lizorkin-Triebel spaces; approximation spaces; trace operators; boundary problems; interpolation; atomic decompositions; refined Sobolev embeddings; anisotropic scales; anisotropic Besov and Lizorkin-Triebel spaces; approximation spaces; trace operators; boundary problems; interpolation; atomic decompositions; refined Sobolev embeddings; anisotropic scales
UR - http://eudml.org/doc/248677
ER -

References

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