Revista Matemática Iberoamericana

Extreme cases of weak type interpolation

Evgeniy Pustylnik

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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 $T:L_{\varphi,E}\to L_{\psi,E}$.

Article information

Source
Rev. Mat. Iberoamericana, Volume 21, Number 2 (2005), 557-576.

Dates
First available in Project Euclid: 11 August 2005

Permanent link to this document
https://projecteuclid.org/euclid.rmi/1123766806

Mathematical Reviews number (MathSciNet)
MR2174916

Zentralblatt MATH identifier
1092.46016

Subjects
Primary: 46B70: Interpolation between normed linear spaces [See also 46M35] 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

Keywords
rearrangement invariant spaces Boyd indices weak interpolation

Citation

Pustylnik, Evgeniy. Extreme cases of weak type interpolation. Rev. Mat. Iberoamericana 21 (2005), no. 2, 557--576. https://projecteuclid.org/euclid.rmi/1123766806


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References

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