| Title:
|
Approximation and entropy numbers of embeddings in weighted Orlicz spaces (English) |
| Author:
|
Edmunds, D. E. |
| Author:
|
Sun, Jiong |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
116 |
| Issue:
|
3 |
| Year:
|
1991 |
| Pages:
|
281-295 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
entropy numbers |
| Keyword:
|
weighted Sobolev spaces |
| Keyword:
|
Orlicz spaces |
| Keyword:
|
Sobolev spaces |
| Keyword:
|
weights |
| Keyword:
|
approximation and entropy numbers |
| MSC:
|
41A46 |
| MSC:
|
46E35 |
| idZBL:
|
Zbl 0751.41019 |
| idMR:
|
MR1126450 |
| DOI:
|
10.21136/MB.1991.126169 |
| . |
| Date available:
|
2009-09-24T20:46:00Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126169 |
| . |
| Reference:
|
[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. MR 0562305 |
| Reference:
|
[2] D. E. Edmunds R. M. Edmunds: Entropy and approximation numbers of embeddings in Orlicz spaces.J. Lond. Math. Soc. (2) 32 (1985), 528-538. MR 0825929, 10.1112/jlms/s2-32.3.528 |
| Reference:
|
[3] D. E. Edmunds W. D. Evans: Orlicz and Sobolev spaces on unbounded domains.Proc. Roy. Soc. A342 (1975), 373-400. MR 0394170 |
| Reference:
|
[4] D. E. Edmunds W. D. Evans: Spectral theory and differential operators.Oxford University Press, Oxford, 1987. MR 0929030 |
| Reference:
|
[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. MR 1106583 |
| Reference:
|
[6] M. Krbec L. Pick: On imbeddings between weighted Orlicz spaces.Zeitschrift Anal. Anwend. (1) 10 (1991), 105-116. MR 1155360 |
| Reference:
|
[7] A. Kufner: Weighted Sobolev spaces.John Wiley and Sons Ltd., 1985. Zbl 0579.35021, MR 0802206 |
| Reference:
|
[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. Zbl 0627.46032, MR 0877105 |
| Reference:
|
[9] M. Namasivayam: Estimates of entropy numbers of embeddings of Sobolev spaces on unbounded domains.Quart. J. Math., Oxford (2) 36 (1985), 231-242. MR 0790483, 10.1093/qmath/36.2.231 |
| Reference:
|
[10] E. W. Stredulinsky: Weighted inequalities and degenerate elliptic partial differential equations.Lecture Notes in Mathematics 1074, Springer-Verlag, Berlin-Heidelberg-New York, 1984. Zbl 0541.35001, MR 0757718 |
| Reference:
|
[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. MR 0766221 |
| Reference:
|
[12] H. Triebel: Interpolation theory, function spaces, differential operators.North-Holland, Amsterdam, 1978. Zbl 0387.46033, MR 0503903 |
| Reference:
|
[13] N. S. Trudinger: On imbeddings into Orlicz spaces and some applications.J. Math. Mech., 17 (1967), 473-484. Zbl 0163.36402, MR 0216286 |
| . |
