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 Funktsional. Anal. i Prilozhen.: Year: Volume: Issue: Page: Find

 Funktsional. Anal. i Prilozhen., 2006, Volume 40, Issue 3, Pages 66–69 (Mi faa744)

Brief communications

The Real Interpolation Method on Couples of Intersections

S. V. Astashkina, P. Sunehagb

a Samara State University
b Uppsala University

Abstract: Suppose that $(X_0,X_1)$ is a Banach couple, $X_0\cap X_1$ is dense in $X_0$ and $X_1$, $(X_0,X_1)_{\theta,q}$ ($0<\theta<1$, $1\le q<\infty$) are the spaces of the real interpolation method, $\psi\in(X_0\cap X_1)^*$, $\psi\ne 0$, is a linear functional, $N=\operatorname{Ker}\psi$, and $N_i$ stands for $N$ with the norm inherited from $X_i$ ($i=0,1$). The following theorem is proved: the norms of the spaces $(N_0,N_1)_{\theta,q}$ and $(X_0,X_1)_{\theta,q}$ are equivalent on $N$ if and only if $\theta\in(0,\alpha)\cup(\beta_\infty,\alpha_0)\cup(\beta_0,\alpha_\infty)\cup(\beta,1)$, where $\alpha$, $\beta$, $\alpha_0$, $\beta_0$, $\alpha_\infty$, and $\beta_\infty$ are the dilation indices of the function $k(t)=\mathcal{K}(t,\psi;X_0^*,X_1^*)$.

Keywords: interpolation space, interpolation of subspaces, interpolation of intersections, real interpolation method, $\mathcal{K}$-functional, dilation index of a function, weighted $L_p$-space

DOI: https://doi.org/10.4213/faa744

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English version:
Functional Analysis and Its Applications, 2006, 40:3, 218–221

Bibliographic databases:

UDC: 517.982.27

Citation: S. V. Astashkin, P. Sunehag, “The Real Interpolation Method on Couples of Intersections”, Funktsional. Anal. i Prilozhen., 40:3 (2006), 66–69; Funct. Anal. Appl., 40:3 (2006), 218–221

Citation in format AMSBIB
\Bibitem{AstSun06} \by S.~V.~Astashkin, P.~Sunehag \paper The Real Interpolation Method on Couples of Intersections \jour Funktsional. Anal. i Prilozhen. \yr 2006 \vol 40 \issue 3 \pages 66--69 \mathnet{http://mi.mathnet.ru/faa744} \crossref{https://doi.org/10.4213/faa744} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2265686} \zmath{https://zbmath.org/?q=an:1123.46017} \elib{https://elibrary.ru/item.asp?id=9296644} \transl \jour Funct. Anal. Appl. \yr 2006 \vol 40 \issue 3 \pages 218--221 \crossref{https://doi.org/10.1007/s10688-006-0033-0} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000241583800007} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33749524624} 

• http://mi.mathnet.ru/eng/faa744
• https://doi.org/10.4213/faa744
• http://mi.mathnet.ru/eng/faa/v40/i3/p66

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This publication is cited in the following articles:
1. Baghdasaryan A.G., “Certain Problems on the Commutativity of Interpolation Functors”, J. Contemp. Math. Anal.-Armen. Aca., 48:3 (2013), 123–138
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