Let φ: R → [0,∞) an integrable function such that φχ(-∞,0) = 0 and φ is decreasing in (0,∞). Let τhf(x) = f(x-h), with h ∈ R {0} and fR(x) = 1/R f(x/R), with R > 0. In this paper we characterize the pair of weights (u, v) such that the operators Mτhφf(x) = supR>0|f| * [τhφ]R(x) are of weak type (p, p) with respect to (u, v), 1 < p < ∞.
@article{urn:eudml:doc:41446,
title = {Two weighted inequalities for convolution maximal operators.},
journal = {Publicacions Matem\`atiques},
volume = {46},
year = {2002},
pages = {119-138},
mrnumber = {MR1904859},
zbl = {1013.42013},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41446}
}
Bernardis, Ana Lucía; Martín-Reyes, Francisco Javier. Two weighted inequalities for convolution maximal operators.. Publicacions Matemàtiques, Tome 46 (2002) pp. 119-138. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41446/