On the range space of Yano's extrapolation theorem and new extrapolation estimates at infinity.
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 re...
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| Tipo de documento: | artigo |
| Estado: | Versão publicada |
| Data de publicação: | 2002 |
| País: | España |
| Recursos: | Universidad de Barcelona |
| Repositório: | Dipòsit Digital de la UB |
| OAI Identifier: | oai:diposit.ub.edu:2445/132424 |
| Acesso em linha: | https://hdl.handle.net/2445/132424 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Anàlisi harmònica Teoria d'operadors Harmonic analysis Operator theory |
| Resumo: | 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. |
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