Logarithmic sobolev spaces on ℝn; entropy numbers, and some applications

Forum Mathematicum

Volumn 12, Issue 3, 2000, Pages 257-313

  Haroske, Dorothee D ^a  

^a FRIEDRICH SCHILLER UNIVERSITY JENA   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040190154     PISSN: 09337741     EISSN: None     Source Type: Journal    
DOI: 10.1515/form.2000.007     Document Type: Article

References (25)

1. Bennett, C. and Rudnick, K.: On Lorentz-Zygmund spaces. Dissertations Math. 175 (1980), 1-72
2. Bennett, C. and Sharpley, R.: Interpolation of Operators. Academic Press, Boston 1988
3. Carl, B.: Entropy numbers, s-numbers and eigenvalue problems. J. Funct. Anal. 41 (1981), 290-306
4. Carl, B. and Stephani, I.: Entropy, compactness and the approximation of operators. Cambridge Univ. Press, Cambridge 1990
5. Carl, B. and Triebel, H.: Inequalities between eigenvalues, entropy numbers and related quantities in Banach spaces. Math. Ann. 251 (1980), 129-133
6. Edmunds, D. E. and Evans, W. D.: Spectral Theory and Differential Operators. Clarendon Press, Oxford 1987
7. Edmunds, D. E., Gurka, P. and Opic, B.: On embeddings of logarithmic Bessel potential spaces. J. Funct. Anal. 146(1) (1997), 116-150
8. Edmunds, D. E. and Netrusov, Yu.: Entropy numbers of embeddings of Sobolev spaces in Zygmund spaces. Studia Math. 128(1) (1998), 71-102
9. Edmunds, D. E. and Triebel, H.: Function Spaces, Entropy Numbers, Differential Operators. Cambridge Univ. Press, Cambridge 1996
10. Haroske, D.: Approximation numbers in some weighted function spaces. J. Approx. Theory, 83(1) (1995), 104-136
11. Haroske, D.: Some limiting embeddings in weighted function spaces and related entropy numbers. Forschungsergebnisse Math/Inf/97/04, Universität Jena, Germany, 1997
12. Haroske, D.: Some logarithmic function spaces, entropy numbers, applications to spectral theory. Dissertationes Math. 373 (1998), 1-59
13. Haroske, D. and Triebel, H.: Entropy numbers in weighted function spaces and eigenvalue distribution of some degenerate pseudodifferential operators I. Math. Nachr. 167 (1994), 131-156
14. Haroske, D. and Triebel, H.: Entropy numbers in weighted function spaces and eigenvalue distribution of some degenerate pseudodifferential operators II. Math. Nachr. 168 (1994), 109-137
15. n; entropy and approximation numbers. A survey of some recent results. An. Univ. Craiova. Ser. Mat. Inform. 24 (1997), 1-44
16. König, H.: Eigenvalue Distribution of Compact Operators. Birkhäuser, Basel 1986
17. Schmeißer, H.-J. and Triebel, H.: Topics in Fourier Analysis and Function Spaces. Wiley, Chichester 1987
18. p,q type. Z. Anal. Anwendungen 14 (1995), 105-140
19. Strichartz, R. S.: A note on Trudingers extension of Sobolev's inequalities. Indiana Univ. Math. J. 21 (1972), 841-842
20. Triebel, H.: Interpolation Theory, Function Spaces, Differential Operators. North-Holland, Amsterdam 1978
21. Triebel, H.: Theory of Function Spaces. Birkhäuser, Basel 1983
22. Triebel, H.: Theory of Function Spaces II. Birkhäuser, Basel 1992
23. Triebel, H.: Approximation numbers and entropy numbers of embeddings of fractional Besov-Sobolev spaces in Orlicz spaces. Proc. London Math. Soc. 66(3) (1993), 589-618
24. p,q spaces. Studia Math. 109(2) (1994), 183-195
25. Trudinger, N. S.: On embeddings into Orlicz spaces and some applications. J. Math. Mech. 17 (1967), 473-483