Approximation and entropy numbers of embeddings in weighted Orlicz spaces

David Eric Edmunds; Jiong Sun

Mathematica Bohemica (1991)

  • Volume: 116, Issue: 3, page 281-295
  • ISSN: 0862-7959

Abstract

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Upper estimates are obtained for approximation and entropy numbers of the embeddings of weighted Sobolev spaces into appropriate weighted Orlicz spaces. Results are given when the underlying space domain is bounded and for certain unbounded domains.

How to cite

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Edmunds, David Eric, and Sun, Jiong. "Approximation and entropy numbers of embeddings in weighted Orlicz spaces." Mathematica Bohemica 116.3 (1991): 281-295. <http://eudml.org/doc/29323>.

@article{Edmunds1991,
abstract = {Upper estimates are obtained for approximation and entropy numbers of the embeddings of weighted Sobolev spaces into appropriate weighted Orlicz spaces. Results are given when the underlying space domain is bounded and for certain unbounded domains.},
author = {Edmunds, David Eric, Sun, Jiong},
journal = {Mathematica Bohemica},
keywords = {entropy numbers; weighted Sobolev spaces; Orlicz spaces; Sobolev spaces; weights; approximation and entropy numbers; entropy numbers; weighted Sobolev spaces; Orlicz spaces},
language = {eng},
number = {3},
pages = {281-295},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Approximation and entropy numbers of embeddings in weighted Orlicz spaces},
url = {http://eudml.org/doc/29323},
volume = {116},
year = {1991},
}

TY - JOUR
AU - Edmunds, David Eric
AU - Sun, Jiong
TI - Approximation and entropy numbers of embeddings in weighted Orlicz spaces
JO - Mathematica Bohemica
PY - 1991
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 116
IS - 3
SP - 281
EP - 295
AB - Upper estimates are obtained for approximation and entropy numbers of the embeddings of weighted Sobolev spaces into appropriate weighted Orlicz spaces. Results are given when the underlying space domain is bounded and for certain unbounded domains.
LA - eng
KW - entropy numbers; weighted Sobolev spaces; Orlicz spaces; Sobolev spaces; weights; approximation and entropy numbers; entropy numbers; weighted Sobolev spaces; Orlicz spaces
UR - http://eudml.org/doc/29323
ER -

References

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  1. M. S. Birman M. S. Solomjak, Quantitative analysis in Sobolev imbedding theorems and applications to spectral theory, Amer. Math. Soc. Transl. (2) 114 (1980), 1 - 132. (1980) MR0562305
  2. D. E. Edmunds R. M. Edmunds, 10.1112/jlms/s2-32.3.528, J. Lond. Math. Soc. (2) 32 (1985), 528-538. (1985) MR0825929DOI10.1112/jlms/s2-32.3.528
  3. D. E. Edmunds W. D. Evans, Orlicz and Sobolev spaces on unbounded domains, Proc. Roy. Soc. A342 (1975), 373-400. (1975) MR0394170
  4. D. E. Edmunds W. D. Evans, Spectral theory and differential operators, Oxford University Press, Oxford, 1987. (1987) MR0929030
  5. D. E. Edmunds A. Kufner, Jiong Sun, Extensions of functions in weighted Sobolev spaces, Rend. Accad. Nat. Sci. XL Mem. Mat. (5) 14, 17 (1990), 327-339. (1990) MR1106583
  6. M. Krbec L. Pick, On imbeddings between weighted Orlicz spaces, Zeitschrift Anal. Anwend. (1) 10 (1991), 105-116. (1991) MR1155360
  7. A. Kufner, Weighted Sobolev spaces, John Wiley and Sons Ltd., 1985. (1985) Zbl0579.35021MR0802206
  8. A. Kufner, Boundary value problems in weighted spaces, Equadiff 6, Lecture Notes in Mathematics 1192, Springer-Verlag, Berlin-Heidelberg-New York, 1986, pp. 35-48. (1986) Zbl0627.46032MR0877105
  9. M. Namasivayam, 10.1093/qmath/36.2.231, Quart. J. Math., Oxford (2) 36 (1985), 231-242. (1985) MR0790483DOI10.1093/qmath/36.2.231
  10. E. W. Stredulinsky, Weighted inequalities and degenerate elliptic partial differential equations, Lecture Notes in Mathematics 1074, Springer-Verlag, Berlin-Heidelberg-New York, 1984. (1984) Zbl0541.35001MR0757718
  11. J.-O. Strömberg R. L. Wheeden, Fractional integrals on weighted H p and L p spaces, Trans. Amer. Math. Soc. 287 (1985), 293-321. (1985) MR0766221
  12. H. Triebel, Interpolation theory, function spaces, differential operators, North-Holland, Amsterdam, 1978. (1978) Zbl0387.46033MR0503903
  13. N. S. Trudinger, On imbeddings into Orlicz spaces and some applications, J. Math. Mech., 17 (1967), 473-484. (1967) Zbl0163.36402MR0216286

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