Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Real interpolation of vector-valued spaces in non-diagonal case


Authors: Irina Asekritova and Natan Krugljak
Journal: Proc. Amer. Math. Soc. 133 (2005), 1665-1675
MSC (2000): Primary 46B70; Secondary 46E30
Published electronically: December 20, 2004
MathSciNet review: 2120255
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that the formula

\begin{displaymath}(l_{p_{0}}^{s_{0}}(A_{0}),...,l_{p_{n}}^{s_{n}}(A_{n})) _{\vec{\theta },q} =l_{q}^{s}((A_{0},...,A_{n})_{\vec{\theta},q}), \end{displaymath}

where $\vec{\theta}=(\theta _{0},...,\theta _{n})$ and $s=\theta _{0}s_{0}+...+\theta _{n}s_{n}$ is correct under the restrictions $ A_{n-1}=A_{n}$ and $s_{n-1}\neq s_{n}.$ It is also true if we suppose that

\begin{displaymath}A_{n}=(A_{0},A_{1},...,A_{n-1})_{\vec{\lambda},p},s_{n}\neq \lambda _{0}s_{0}+\lambda _{1}s_{1}+...+\lambda _{n-1}s_{n-1}, \end{displaymath}

and the spaces $A_{0},A_{1},...,A_{n-1}$ are functional Banach or quasi-Banach lattices on the same measure space $(\Omega ,\mu ).$


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 46B70, 46E30

Retrieve articles in all journals with MSC (2000): 46B70, 46E30


Additional Information

Irina Asekritova
Affiliation: School of Mathematics and Systems Engineering, Vaxjo University, SE 351 93, Vaxjo, Sweden
Email: irina.asekritova@msi.vxu.se

Natan Krugljak
Affiliation: Department of Mathematics, LuleåUniversity of Technology, SE 972 33, Luleå, Sweden
Email: natan@sm.luth.se

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07714-7
PII: S 0002-9939(04)07714-7
Keywords: Real interpolation, vector-valued spaces
Received by editor(s): September 16, 2003
Published electronically: December 20, 2004
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.



Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia