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Entropy numbers in sequence spaces with an application to weighted function spaces. (English) Zbl 1145.47017

Author’s summary: “We determine the exact asymptotic behaviour of entropy numbers of diagonal operators from \(\ell_p\) to \(\ell_q\), \(0<q<p \leqslant \infty \), under mild regularity conditions on the generating diagonal sequence. On one hand, this is a quantitative version of Pitt’s theorem for diagonal operators, and on the other hand it is a limiting case of results by Carl. An application to embeddings of weighted Besov and Triebel-Lizorkin spaces is also given.”
Note: This continues previous work of the author on entropy numbers.

MSC:

47B06 Riesz operators; eigenvalue distributions; approximation numbers, \(s\)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
46B45 Banach sequence spaces
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References:

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