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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2006, Volume 255, Pages 170–179
(Mi tm261)
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This article is cited in 8 scientific papers (total in 8 papers)
Entropy Numbers in Weighted Function Spaces. The Case of Intermediate Weights
T. Kühn Universität Leipzig
Abstract:
The exact asymptotic behavior of the entropy numbers of compact embeddings of weighted Besov spaces is known in many cases, in particular for power-type weights and logarithmic weights. Here we consider intermediate weights that are strictly between these two scales; a typical example is $w(x)=\exp\bigl(\sqrt {\log (1+|x|)}\,\bigr)$. For such weights we prove almost optimal estimates of the entropy numbers $e_k\bigl (\mathrm{id}:B^{s_1}_{p_1 q_1}(\mathbb R^d,w)\to B^{s_2}_{p_2 q_2}(\mathbb R^d)\bigr)$.
Received in December 2005
Citation:
T. Kühn, “Entropy Numbers in Weighted Function Spaces. The Case of Intermediate Weights”, Function spaces, approximation theory, and nonlinear analysis, Collected papers, Trudy Mat. Inst. Steklova, 255, Nauka, MAIK «Nauka/Inteperiodika», M., 2006, 170–179; Proc. Steklov Inst. Math., 255 (2006), 159–168
Linking options:
https://www.mathnet.ru/eng/tm261 https://www.mathnet.ru/eng/tm/v255/p170
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Abstract page: | 246 | Full-text PDF : | 93 | References: | 39 |
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