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Entropy and approximation numbers of limiting embeddings; an approach via Hardy inequalities and quadratic forms. (English) Zbl 1242.47018
Let $B$ be the unit ball in $\bbfR^{n}$. The paper deals with the continuous embeddings of a special weighted Sobolev space of functions defined on $B$ into the Lebesgue space of complex-valued measurable functions on $B$. The weights involve log-terms. In the case where the embeddings are compact, some two-sided estimates for the entropy numbers and approximation numbers are proved.

47B06Riesz operators; eigenvalue distributions; approximation numbers, $s$-numbers etc.of operators
41A46Approximation by arbitrary nonlinear expressions; widths and entropy
47B38Operators on function spaces (general)
Full Text: DOI
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