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July, 2005 Extreme cases of weak type interpolation
Evgeniy Pustylnik
Rev. Mat. Iberoamericana 21(2): 557-576 (July, 2005).

Abstract

We consider quasilinear operators $T$ of {\it joint weak type} $(a,b;p,q)$ (in the sense of [Bennett, Sharpley: Interpolation of operators, Academic Press, 1988]) and study their properties on spaces $L_{\varphi,E}$ with the norm $\|\varphi(t)f^*(t) \|_{\tilde E}$, where $\tilde E$ is arbitrary rearrangement-invariant space with respect to the measure $dt/t$. A space $L_{\varphi,E}$ is said to be ``close" to one of the endpoints of interpolation if the corresponding Boyd index of this space is equal to $1/a$ or to $1/p$. For all possible kinds of such ``closeness", we give sharp estimates for the function $\psi(t)$ so as to obtain that every $T:L_{\varphi,E}\to L_{\psi,E}$.

Citation

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Evgeniy Pustylnik. "Extreme cases of weak type interpolation." Rev. Mat. Iberoamericana 21 (2) 557 - 576, July, 2005.

Information

Published: July, 2005
First available in Project Euclid: 11 August 2005

zbMATH: 1092.46016
MathSciNet: MR2174916

Subjects:
Primary: 46B70 , 46E30

Keywords: Boyd indices , rearrangement invariant spaces , weak interpolation

Rights: Copyright © 2005 Departamento de Matemáticas, Universidad Autónoma de Madrid

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Vol.21 • No. 2 • July, 2005
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