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Approximation Numbers in Some Weighted Function Spaces

✍ Scribed by D. Haroske

Publisher: Elsevier Science
Year: 1995
Tongue: English
Weight: 896 KB
Volume: 83
Category: Article
ISSN: 0021-9045
DOI: 10.1006/jath.1995.1111

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✦ Synopsis

In this paper we study weighted function spaces of type (B_{p, q}^{r}\left(\mathbb{R}^{n}, w(x)\right)) and (F_{p, 4}^{s}\left(\mathbb{R}^{\prime \prime}, w(x)\right)) where (w(x)) is a weight function of at most polynomial growth. preferably (w(x)=\left(1+|x|^{2}\right)^{x^{2}}) with (\alpha \in \mathbb{R}). The main result deals with estimates for the approximation numbers of compact embeddings between spaces of this type. Furthermore we are concerned with the dependence of the approximation numbers (a_{k}) of compact embeddings between function spaces (B_{p, q}^{s}(\Omega)) and (F_{p, q}^{s}(\Omega)) on an underlying domain (\Omega). " 1945 Academic Press. Inc.

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