Zawartość
Pełne teksty:
Warianty tytułu
Abstrakty
CONTENTS
Introduction...........................................................5
1. Preliminaries.....................................................6
Spaces on ℝⁿ......................................................6
Atomic decompositions........................................8
Spaces on domains...........................................10
Embeddings.......................................................11
Entropy numbers................................................11
2. Sharpness.......................................................13
3. Lipschitz embedding, entropy numbers...........21
4. Comparison with related results......................30
Embeddings.......................................................30
Entropy numbers...............................................36
Estimate from above..........................................37
References.........................................................42
Introduction...........................................................5
1. Preliminaries.....................................................6
Spaces on ℝⁿ......................................................6
Atomic decompositions........................................8
Spaces on domains...........................................10
Embeddings.......................................................11
Entropy numbers................................................11
2. Sharpness.......................................................13
3. Lipschitz embedding, entropy numbers...........21
4. Comparison with related results......................30
Embeddings.......................................................30
Entropy numbers...............................................36
Estimate from above..........................................37
References.........................................................42
Słowa kluczowe
Tematy
Kategoryzacja MSC:
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne
tom/nr w serii:
380
Liczba stron
43
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCCLXXX
Daty
wydano
1999
otrzymano
1998-04-24
poprawiono
1998-08-13
Twórcy
autor
- CMAIA, University of Sussex at Brighton, Falmer, Brighton BN1 9QH, United Kingdom
autor
- Mathematical Institute, Friedrich-Schiller-University, D-07740 Jena, Germany
Bibliografia
- [1] C. Bennett and R. Sharpley, Interpolation of Operators, Academic Press, Boston, 1988.
- [2] J. Bourgain, A. Pajor, S. J. Szarek and N. Tomczak-Jaegermann, On the duality problem for entropy numbers of operators, in: Geometric Aspects of Functional Analysis (1987-88), J. Lindenstrauss and V. D. Milman (eds.), Lecture Notes in Math. 1376, Springer, 1989, 50-63.
- [3] H. Brézis and S. Wainger, A note on limiting cases of Sobolev embeddings and convolution inequalities, Comm. Partial Differential Equations 5 (1980), 773-789.
- [4] B. Carl and I. Stephani, Entropy, Compactness and the Approximation of Operators, Cambridge Univ. Press, Cambridge, 1990.
- [5] R. DeVore and G. G. Lorentz, Constructive Approximation, Grundlehren Math. Wiss. 303, Springer, Berlin, 1993.
- [6] D. E. Edmunds and W. D. Evans, Spectral Theory and Differential Operators, Clarendon Press, Oxford, 1987.
- [7] D. E. Edmunds, P. Gurka and B. Opic, On embeddings of logarithmic Bessel potential spaces, J. Funct. Anal. 146 (1997), 116-150.
- [8] D. E. Edmunds, P. Gurka and B. Opic, Optimality of embeddings of logarithmic Bessel potential spaces, to appear.
- [9] D. E. Edmunds and M. Krbec, Two limiting cases of Sobolev imbeddings, Houston J. Math. 21 (1995), 119-128.
- [10] D. E. Edmunds and H. Triebel, Entropy numbers and approximation numbers in function spaces, Proc. London Math. Soc. (3) 58 (1989), 137-152.
- [11] D. E. Edmunds and H. Triebel, Entropy numbers and approximation numbers in function spaces II, Proc. London Math. Soc. (3) 64 (1992), 153-169.
- [12] D. E. Edmunds and H. Triebel, Function Spaces, Entropy Numbers, Differential Operators, Cambridge Univ. Press, Cambridge, 1996.
- [13] M. Frazier and B. Jawerth, A discrete transform and decomposition of distribution spaces, J. Funct. Anal. 93 (1990), 34-170.
- [14] D. Haroske and H. Triebel, Entropy numbers in weighted function spaces and eigenvalue distribution of some degenerate pseudodifferential operators I, Math. Nachr. 167 (1994), 131-156.
- [15] H. König, Eigenvalue Distribution of Compact Operators, Birkhäuser, Basel, 1986.
- [16] H.-G. Leopold, Limiting embeddings and entropy numbers, Forschungsergebnisse Math/Inf/98/05, Universität Jena, Germany, 1998.
- [17] A. Pietsch, Eigenvalues and s-Numbers, Akad. Verlagsgesellschaft Geest & Portig, Leipzig, 1987.
- [18] W. Sickel and H. Triebel, Hölder inequalities and sharp embeddings in function spaces of $B^s_{p,q}$ and $F^s_{p,q}$ type, Z. Anal. Anwendungen 14 (1995), 105-140.
- [19] H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North-Holland, Amsterdam, 1978.
- [20] H. Triebel, Spaces of Besov-Hardy-Sobolev type, Teubner, Leipzig, 1978.
- [21] H. Triebel, Theory of Function Spaces, Birkhäuser, Basel, 1983.
- [22] H. Triebel, Theory of Function Spaces II, Birkhäuser, Basel, 1992.
- [23] H. Triebel, Approximation numbers and entropy numbers of embeddings of fractional Besov-Sobolev spaces in Orlicz spaces, Proc. London Math. Soc. (3) 66 (1993), 589-618.
- [24] H. Triebel, Fractals and Spectra, Birkhäuser, Basel, 1997.
Języki publikacji
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Uwagi
1991 Mathematics Subject Classification: 26A16, 46E35, 41A46, 46E15.
Identyfikator YADDA
bwmeta1.element.zamlynska-17126c89-a594-4107-82bf-95c4741d8313
Identyfikatory
ISSN
0012-3862
Kolekcja
DML-PL
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