✦ LIBER ✦
Embedding vector-valued Besov spaces into spaces of γ -radonifying operators
✍ Scribed by Nigel Kalton; Jan van Neerven; Mark Mark; Lutz Weis
- Publisher
- John Wiley and Sons
- Year
- 2008
- Tongue
- English
- Weight
- 213 KB
- Volume
- 281
- Category
- Article
- ISSN
- 0025-584X
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
It is shown that a Banach space E has type p if and only for some (all) d ≥ 1 the Besov space B^(1/p – 1/2)d^ ~p,p~ (ℝ^d^ ; E) embeds into the space γ (L^2^(ℝ^d^ ), E) of γ ‐radonifying operators L^2^(ℝ^d^ ) → E. A similar result characterizing cotype q is obtained. These results may be viewed as E ‐valued extensions of the classical Sobolev embedding theorems. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)