2007 Volume 59 Issue 2 Pages 323-349
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.
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