Some equivalent characterizations for boundedness of maximal singular integral operators on spaces of homogeneous type are given via certain norm inequalities on John-Strömberg sharp maximal functions and without resorting the boundedness of these operators themselves. As a corollary, the results of Grafakos on Euclidean spaces are generalized to spaces of homogeneous type. Moreover, applications to maximal Monge-Ampère singular integral operators and maximal Nagel-Stein singular integral operators on certain specific smooth manifolds are also presented.
Publié le : 2007-04-14
Classification:
space of homogeneous type,
maximal singular integral,
Monge-Ampère singular integral operator,
Nagel-Stein singular integral operator,
42B20,
47A30,
43A99
@article{1191247590,
author = {HU, Guoen and YANG, Dachun and YANG, Dongyong},
title = {Boundedness of maximal singular integral operators on spaces of homogeneous type and its applications},
journal = {J. Math. Soc. Japan},
volume = {59},
number = {1},
year = {2007},
pages = { 323-349},
language = {en},
url = {http://dml.mathdoc.fr/item/1191247590}
}
HU, Guoen; YANG, Dachun; YANG, Dongyong. Boundedness of maximal singular integral operators on spaces of homogeneous type and its applications. J. Math. Soc. Japan, Tome 59 (2007) no. 1, pp. 323-349. http://gdmltest.u-ga.fr/item/1191247590/