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Article

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Published version

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2002

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/132424

On the range space of Yano's extrapolation theorem and new extrapolation estimates at infinity.

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https://doi.org/10.5565/PUBLMAT_Esco02_02

Abstract

Given a sublinear operator T satisfying that !Tf!Lp(ν) ≤ C p−1 !f!Lp(µ), for every 1 < p ≤ p0, with C independent of f and p, it was proved in [C] that sup r>0 ! ∞ 1/r λν T f (y) dy 1 + log+ r ! ' M |f(x)|(1 + log+ |f(x)|) dµ(x). This estimate implies that T : L log L → B, where B is a rearrangement invariant space. The purpose of this note is to give several characterizations of the space B and study its associate space. This last information allows us to formulate an extrapolation result of Zygmund type for linear operators satisfying !Tf!Lp(ν) ≤ Cp!f!Lp(µ), for every p ≥ p0.

Subject

Anàlisi harmònica, Teoria d'operadors

Subject (English)

Harmonic analysis, Operator theory

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Articles publicats en revistes (Matemàtiques i Informàtica)

Citation

CARRO ROSSELL, María Jesús. On the range space of Yano's extrapolation theorem and new extrapolation estimates at infinity. Publicacions Matemàtiques. 2002. Vol. Extra volume, pags. 27-37. ISSN 0214-1493. [consulted: 16 of August of 2026]. Available at: https://hdl.handle.net/2445/132424

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