Geodesic
Approximation and entropy numbers of embeddings in weighted Orlicz spaces
Mathematica Bohemica, Tome 116 (1991) no. 3, pp. 281-295

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MR Zbl
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.
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.
DOI : 10.21136/MB.1991.126169
Classification : 41A46, 46E35
Keywords: entropy numbers; weighted Sobolev spaces; Orlicz spaces; Sobolev spaces; weights; approximation and entropy numbers 
Edmunds, D. E.; Sun, Jiong. Approximation and entropy numbers of embeddings in weighted Orlicz spaces. Mathematica Bohemica, Tome 116 (1991) no. 3, pp. 281-295. doi: 10.21136/MB.1991.126169
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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. | MR

[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. | DOI | MR

[3] D. E. Edmunds W. D. Evans: Orlicz and Sobolev spaces on unbounded domains. Proc. Roy. Soc. A342 (1975), 373-400. | MR

[4] D. E. Edmunds W. D. Evans: Spectral theory and differential operators. Oxford University Press, Oxford, 1987. | MR

[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

[6] M. Krbec L. Pick: On imbeddings between weighted Orlicz spaces. Zeitschrift Anal. Anwend. (1) 10 (1991), 105-116. | MR

[7] A. Kufner: Weighted Sobolev spaces. John Wiley and Sons Ltd., 1985. | MR | Zbl

[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. | MR | Zbl

[9] M. Namasivayam: Estimates of entropy numbers of embeddings of Sobolev spaces on unbounded domains. Quart. J. Math., Oxford (2) 36 (1985), 231-242. | DOI | MR

[10] E. W. Stredulinsky: Weighted inequalities and degenerate elliptic partial differential equations. Lecture Notes in Mathematics 1074, Springer-Verlag, Berlin-Heidelberg-New York, 1984. | MR | Zbl

[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

[12] H. Triebel: Interpolation theory, function spaces, differential operators. North-Holland, Amsterdam, 1978. | MR | Zbl

[13] N. S. Trudinger: On imbeddings into Orlicz spaces and some applications. J. Math. Mech., 17 (1967), 473-484. | MR | Zbl

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