New sufficient conditions on the weight functions u(.) and v(.) are given in order that the fractional maximal [resp. integral] operator Ms [resp. Is], 0 ≤ s < n, [resp. 0 < s < n] sends the weighted Lebesgue space Lp(v(x)dx) into Lp(u(x)dx), 1 < p < ∞. As a consequence a characterization for this estimate is obtained whenever the weight functions are radial monotone.
@article{urn:eudml:doc:41336,
title = {Two weight norm inequality for the fractional maximal operator and the fractional integral operator.},
journal = {Publicacions Matem\`atiques},
volume = {42},
year = {1998},
pages = {81-101},
mrnumber = {MR1628142},
zbl = {0931.42011},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41336}
}
Rakotondratsimba, Yves. Two weight norm inequality for the fractional maximal operator and the fractional integral operator.. Publicacions Matemàtiques, Tome 42 (1998) pp. 81-101. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41336/