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http://hdl.handle.net/2445/132424
Title: | On the range space of Yano's extrapolation theorem and new extrapolation estimates at infinity. |
Author: | Carro Rossell, María Jesús |
Keywords: | Anàlisi harmònica Teoria d'operadors Harmonic analysis Operator theory |
Issue Date: | 2002 |
Publisher: | Universitat Autònoma de Barcelona |
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. |
Note: | Reproducció del document publicat a: https://doi.org/10.5565/PUBLMAT_Esco02_02 |
It is part of: | Publicacions Matemàtiques, 2002, vol. Extra volume, num. , p. 27-37 |
URI: | http://hdl.handle.net/2445/132424 |
Related resource: | https://doi.org/10.5565/PUBLMAT_Esco02_02 |
ISSN: | 0214-1493 |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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510444.pdf | 227.39 kB | Adobe PDF | View/Open |
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