Let $T$ be a sublinear operator such that $(Tf)^*(t)\le h(t, \|f\|_1)$
for some positive function $h(t,s)$ and every function $f$
such that $\|f\|_{\infty}\le 1$. Then, we show that $T$ can be
extended continuously from a logarithmic type space into a
weighted weak Lorentz space. This type of result is connected with
the theory of restricted weak type extrapolation and extends a
recent result of Arias-de-Reyna concerning the pointwise
convergence of Fourier series to a much more general context.
Publié le : 2004-03-14
Classification:
rearrangement inequality,
real interpolation,
Banach couples,
extrapolation theory,
Carleson's operator,
46M35,
47A30
@article{1080928423,
author = {Carro, Mar\'\i a J. and Mart\'\i n, Joaquim},
title = {Endpoint estimates from restricted rearrangement inequalities},
journal = {Rev. Mat. Iberoamericana},
volume = {20},
number = {1},
year = {2004},
pages = { 131-150},
language = {en},
url = {http://dml.mathdoc.fr/item/1080928423}
}
Carro, María J.; Martín, Joaquim. Endpoint estimates from restricted rearrangement inequalities. Rev. Mat. Iberoamericana, Tome 20 (2004) no. 1, pp. 131-150. http://gdmltest.u-ga.fr/item/1080928423/