On the range space of Yano's extrapolation theorem and new extrapolation estimates at infinity
Carro, María J. (Universitat de Barcelona. Departament de Matemàtica Aplicada i Anàlisi)

Data:	2002
Resum:	Given a sublinear operator T satisfying that T f 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 ∞ λν f (y) dy T 1/r sup |f (x)|(1 + log+ |f (x)|) dµ(x). r>0 1 + log+ r M This estimate implies that T : L log L → B, where B is a re- arrangement 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 extrap- olation result of Zygmund type for linear operators satisfying T f Lp (ν) ≤q Cp f Lp (µ), for every p ≥ p0.
Drets:	Tots els drets reservats.
Llengua:	Anglès
Document:	Article ; recerca ; Versió publicada
Matèria:	Extrapolation ; Boundeness of operators ; Endpoint estimates
Publicat a:	Publicacions matemàtiques, Vol. Extra (2002) , p. 27-37, ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/38030
DOI: 10.5565/PUBLMAT_Esco02_02

11 p, 227.4 KB

El registre apareix a les col·leccions:
Articles > Articles publicats > Publicacions matemàtiques
Articles > Articles de recerca