This is an announcement for the paper "Embedding vector-valued Besov spaces into spaces of $\gamma$-radonifying operators" by Nigel Kalton, Jan van Neerven, Mark Veraar, and Lutz Weis.
Abstract: It is shown that a Banach space $E$ has type $p$ if and only for some (all) $d\ge 1$ the Besov space $B_{p,p}^{(\frac1p-\frac12)d}(\R^d;E)$ embeds into the space $\g(L^2(\R^d),E)$ of $\g$-radonifying operators $L^2(\R^d)\to E$. A similar result characterizing cotype $q$ is obtained. These results may be viewed as $E$-valued extensions of the classical Sobolev embedding theorems.
Archive classification: Functional Analysis
Mathematics Subject Classification: 46B09; 46E35; 46E40
Remarks: To appear in Mathematische Nachrichten
The source file(s), besovArxiv.tex: 51566 bytes, is(are) stored in gzipped form as 0610620.gz with size 16kb. The corresponding postcript file has gzipped size 82kb.
Submitted from: m.c.veraar@tudelft.nl
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http://arXiv.org/abs/math.FA/0610620
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