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... [check the paper abstract for the formula]
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.
[Proceedings of the 6th International Conference on Harmonic Analysis and Partial Differential Equations, El Escorial (Madrid), 2002].
@article{urn:eudml:doc:41816,
title = {On the range space of Yano's extrapolation theorem and new extrapolation estimates at infinity.},
journal = {Publicacions Matem\`atiques},
volume = {46},
year = {2002},
pages = {27-37},
zbl = {1028.46107},
mrnumber = {MR1964814},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41816}
}
Carro, María Jesús. On the range space of Yano's extrapolation theorem and new extrapolation estimates at infinity.. Publicacions Matemàtiques, Tome 46 (2002) pp. 27-37. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41816/