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Abstrakty
We prove asymptotic formulas for the behaviour of approximation numbers of Sobolev embeddings between Besov and Triebel-Lizorkin spaces of radial distributions.
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Rocznik
Strony
237--255
Opis fizyczny
Bibliogr. 21 poz.
Twórcy
autor
- Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland
autor
- Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland
Bibliografia
- [CS] B. Carl and I. Stephani, Entropy, compactness and the approximation of operators. Cambridge Univ. Press, Cambridge, 1990.
- [Cae] A. M. Caetano, About approximation numbers in Function spaces, J. Approx. Theory 94 (1998), 383-395.
- [CGM] S. Coleman, V. Glazer and A. Martin, Action minima among solutions to a class of euclidean scalar field equations, Comm. in Math. Physics 58 (1978), 211-221.
- [ET 1] D. E. Edmunds and H. Triebel, Entropy numbers and approximation numbers in function spaces, Proc. London Math. Soc. 58 (1989), 137-152.
- [ET 2] D. E. Edmunds and H. Triebel, Entropy numbers and approximation numbers in function spaces II, Proc. London Math. Soc. 64 (1992), 153-169.
- [ET] D. E. Edmunds and H. Triebel, Function spaces, entropy numbers, differential operators, Cambridge Univ. Press, Cambridge, 1996.
- [EF] J. Epperson and M. Frazier, An almost orthogonal radial wavelet expansion for radial distributions, J. Fourier Anal. Appl. 1 (1995), 311-353.
- [FJ1] M. Frazier and B. Jawerth, A discrete transform and decomposition of distribution spaces, J. Funct. Anal. 93 (1990), 34-170.
- [Har 1] D. Haroske, Approximation numbers in some weighted function spaces, Journal of Approx. Theory 83 (1995), 104-136.
- [Har 2] D. Haroske, Embeddings of some weighted function spaces on Rn; entropy and approximation numbers, An. Univ. Craiova, Ser. Mat. Inform. 24 (1997), 1-44.
- [HT 1] D. Haroske and H. Triebel, Entropy numbers in weighted function spaces and eigenvalue distributions of some degenerate pseudodifferential operators I, Math. Nachr. 167 (1994), 131-156.
- [Kön] H. König, Eigenvalue Distribution of Compact Operators, Birkhäuser, Basel, 1986.
- [KLSS] T. Kühn, H.-G. Leopold, W. Sickel and L. Skrzypczak, Entropy numbers of Sobolev embeddings of radial Besov spaces, J. Approx. Theory 121 (2003), 244-268.
- [Lio] P.-L. Lions, Symétrie et compacité dans les espaces de Sobolev, J. Funct. Anal. 49 (1982), 315-334.
- [Pe] J. Peetre, New Thoughts on Besov spaces, Duke Univ. Math. Series, Duke Univ., Durham, 1976.
- [Pi] A. Pietsch, Eigenvalues and s-numbers, Akad. Verlagsges, Geest & Portig, Leipzig, 1987.
- [SS] W. Sickel and L. Skrzypczak, Radial subspaces of Besov and Lizorkin-Triebel Classes: Extended Strauss Lemma and Compactness of Embedding, J. Fourier Anal. App. 6 (2000), 639-662.
- [Skr] L. Skrzypczak, On approximation numbers of Sobolev embeddings of weighted function spaces, (submitted).
- [Str] W. A. Strauss, Existence of solitary waves in higher dimensions, Comm. in Math. Physics 55 (1977), 149-162.
- [Tr 1] H. Triebel, Interpolation theory, function spaces, differential operators, North-Holland, Amsterdam, 1978.
- [Tr 2] H. Triebel, Theory of Function Spaces, Birkhäuser, Basel, 1983.
Uwagi
Dedicated to our teacher Prof. Julian Musielak on the occasion of his 75th birthday.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BUS2-0007-0061