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Embedding vector‐valued Besov spaces into spaces of γ ‐radonifying operators
Author(s) -
Kalton Nigel,
van Neerven Jan,
Mark Mark,
Weis Lutz
Publication year - 2008
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200510598
Subject(s) - mathematics , embedding , besov space , banach space , sobolev space , pure mathematics , interpolation space , space (punctuation) , type (biology) , functional analysis , computer science , ecology , biochemistry , chemistry , artificial intelligence , biology , gene , operating system
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) dp , 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)
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