Embedding vector-valued Besov spaces into spaces of $\gamma$-radonifying operators

Nigel Kalton; Jan van Neerven; Mark Veraar; Lutz Weis

Embedding vector-valued Besov spaces into spaces of $\gamma$-radonifying operators

Functional Analysis 2007-05-23 v1

Authors: Nigel Kalton , Jan van Neerven , Mark Veraar , 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.

Keywords

besov spaces gamma-radonifying operators banach space type banach space cotype sobolev embedding

Cite

@article{arxiv.math/0610620,
  title  = {Embedding vector-valued Besov spaces into spaces of $\gamma$-radonifying operators},
  author = {Nigel Kalton and Jan van Neerven and Mark Veraar and Lutz Weis},
  journal= {arXiv preprint arXiv:math/0610620},
  year   = {2007}
}

Comments

To appear in Mathematische Nachrichten

Embedding vector-valued Besov spaces into spaces of $\gamma$-radonifying operators

Abstract

Keywords

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