Approximation by functions of compact support in Besov-Triebel-Lizorkin spaces on irregular domains

António Caetano

Studia Mathematica (2000)

  • Volume: 142, Issue: 1, page 47-63
  • ISSN: 0039-3223

Abstract

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General Besov and Triebel-Lizorkin spaces on domains with irregular boundary are compared with the completion, in those spaces, of the subset of infinitely continuously differentiable functions with compact support in the same domains. It turns out that the set of parameters for which those spaces coincide is strongly related to the fractal dimension of the boundary of the domains.

How to cite

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Caetano, António. "Approximation by functions of compact support in Besov-Triebel-Lizorkin spaces on irregular domains." Studia Mathematica 142.1 (2000): 47-63. <http://eudml.org/doc/216788>.

@article{Caetano2000,
abstract = {General Besov and Triebel-Lizorkin spaces on domains with irregular boundary are compared with the completion, in those spaces, of the subset of infinitely continuously differentiable functions with compact support in the same domains. It turns out that the set of parameters for which those spaces coincide is strongly related to the fractal dimension of the boundary of the domains.},
author = {Caetano, António},
journal = {Studia Mathematica},
keywords = {general Besov and Triebel-Lizorkin spaces on domains with irregular boundary; infinitely continuously differentiable functions with compact support},
language = {eng},
number = {1},
pages = {47-63},
title = {Approximation by functions of compact support in Besov-Triebel-Lizorkin spaces on irregular domains},
url = {http://eudml.org/doc/216788},
volume = {142},
year = {2000},
}

TY - JOUR
AU - Caetano, António
TI - Approximation by functions of compact support in Besov-Triebel-Lizorkin spaces on irregular domains
JO - Studia Mathematica
PY - 2000
VL - 142
IS - 1
SP - 47
EP - 63
AB - General Besov and Triebel-Lizorkin spaces on domains with irregular boundary are compared with the completion, in those spaces, of the subset of infinitely continuously differentiable functions with compact support in the same domains. It turns out that the set of parameters for which those spaces coincide is strongly related to the fractal dimension of the boundary of the domains.
LA - eng
KW - general Besov and Triebel-Lizorkin spaces on domains with irregular boundary; infinitely continuously differentiable functions with compact support
UR - http://eudml.org/doc/216788
ER -

References

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  2. [2] A. M. Caetano, On fractals which are not so terrible, in preparation. Zbl1002.28010
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  7. [7] P. Mattila, Geometry of Sets and Measures in Euclidean Spaces, Cambridge Univ. Press, Cambridge, 1995. Zbl0819.28004
  8. [8] N. G. Meyers, Continuity properties of potentials, Duke Math. J. 42 (1975), 157-166. Zbl0334.31004
  9. [9] H. Triebel, Theory of Function Spaces, Birkhäuser, Basel, 1983. 
  10. [10] H. Triebel, Fractals and Spectra, Birkhäuser, Basel, 1997. 
  11. [11] H. Triebel, Decompositions of function spaces, in: Topics in Nonlinear Analysis, the Herbert Amann Anniversary Volume, Birkhäuser, Basel, 1999, 691-730. Zbl0920.46027
  12. [12] H. Triebel, Function spaces and Dirichlet problems in fractal domains, preprint, Jena, 1999. 
  13. [13] H. Triebel and H. Winkelvoss, Intrinsic atomic characterizations of function spaces on domains, Math. Z. 221 (1996), 647-673. Zbl0843.46022
  14. [14] H. Wallin, The trace to the boundary of Sobolev spaces on a snowflake, Manuscripta Math. 73 (1991), 117-125. Zbl0793.46015

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