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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

 

The quasinormed Neumann-Schatten ideals and embedding theorems for the generalized Lions-Peetre spaces of means


Author: V. I. Ovchinnikov
Translated by: the author
Original publication: Algebra i Analiz, tom 22 (2010), nomer 4.
Journal: St. Petersburg Math. J. 22 (2011), 669-681
MSC (2010): Primary 46M35, 46B70
Published electronically: May 3, 2011
MathSciNet review: 2768965
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Abstract: For the spaces $ \varphi(X_0,X_1)_{p_0,p_1}$, which generalize the spaces of means introduced by Lions and Peetre to the case of functional parameters, necessary and sufficient conditions are found for embedding when all parameters (the function $ \varphi$ and the numbers $ 1\leq p_0$, $ p_1\leq \infty)$ vary. The proof involves a description of generalized Lions-Peetre spaces in terms of orbits and co-orbits of von Neumann-Schatten ideals (including quasinormed ideals).


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Additional Information

V. I. Ovchinnikov
Affiliation: Voronezh State University, Universitetskaya Ploshchad’, 1, Voronezh 394006, Russia
Email: vio@comch.ru

DOI: http://dx.doi.org/10.1090/S1061-0022-2011-01162-8
PII: S 1061-0022(2011)01162-8
Keywords: Embedding theorems, method of means, functional parameter, generalized spaces
Received by editor(s): May 20, 2009
Published electronically: May 3, 2011
Additional Notes: Supported by RFBR (grant no. 07-01-00131)
Article copyright: © Copyright 2011 American Mathematical Society