Journal of the Mathematical Society of Japan

Boundedness of maximal singular integral operators on spaces of homogeneous type and its applications

Guoen HU, Dachun YANG, and Dongyong YANG

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Abstract

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.

Article information

Source
J. Math. Soc. Japan, Volume 59, Number 2 (2007), 323-349.

Dates
First available in Project Euclid: 1 October 2007

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1191247590

Digital Object Identifier
doi:10.2969/jmsj/05920323

Mathematical Reviews number (MathSciNet)
MR2325688

Zentralblatt MATH identifier
1133.42020

Subjects
Primary: 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.)
Secondary: 47A30: Norms (inequalities, more than one norm, etc.) 43A99: None of the above, but in this section

Keywords
space of homogeneous type maximal singular integral Monge-Ampère singular integral operator Nagel-Stein singular integral operator

Citation

HU, Guoen; YANG, Dachun; YANG, Dongyong. Boundedness of maximal singular integral operators on spaces of homogeneous type and its applications. J. Math. Soc. Japan 59 (2007), no. 2, 323--349. doi:10.2969/jmsj/05920323. https://projecteuclid.org/euclid.jmsj/1191247590


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