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Journal of Zhejiang University SCIENCE A 2001 Vol.2 No.3 P.257-260

http://doi.org/10.1631/jzus.2001.0257


A CLASS OF MARCINKIEWICZ INTEGRAL OPERATORS ON PRODUCT DOMAINS


Author(s):  YING Yi-ming, LIU Xiao-feng

Affiliation(s):  Department of Mathematics, Zhejiang University, Hangzhou 310028, China

Corresponding email(s): 

Key Words:  Marcinkiewicz integral operator, rough kernel, product domains, square functions


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YING Yi-ming, LIU Xiao-feng. A CLASS OF MARCINKIEWICZ INTEGRAL OPERATORS ON PRODUCT DOMAINS[J]. Journal of Zhejiang University Science A, 2001, 2(3): 257-260.

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Abstract: 
In this paper, the author proves that the Lp-boundedness of the Marcinkiewicz integral μΩ on product domains Rn×Rm; for Ω(1)∩(5) improves the result of Chen et al. (2000).

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

[1] Chen Jiecheng, Fan Dashan, Pan Yibiao, 2001. A note on Marcinkiewicz integral operator. Math. Nachr. (accepted).

[2] Chen Jiecheng, Fan Dashan, Pan Yibiao, 2000. Lp-boundedness of rough Marcinkiewicz integralon product domains. Chinese Annals of Math.(Ser. A), 21(1):39-44.

[3] Ding Yong. 1998. The Marcinkiewicz integral operator with Hardy space function kernel on productdomains, Math. Proc. of Camb. Phil. Soc. 123(2):337-343.

[4] Duoandikotxea, J., 1986. Multiple singular integrals and maximal functions along hyperplaces. Ann.Inst. Fourier, Grenoble 36(4):185-206.

[5] Fefferman, R. Stein, E.M., 1982. Singular integrals on product spaces. Advance in Math. 45:117-143.

[6] Frazier, M., 1991. Littlewood-Paley theory and the study of function spaces. CBMS No.79, AMS, Providence, Rhode Island.

[7] Grafakos, L., Stefanov, A., 1998. Lp bounds for singular integrals and maxmal singular integralswith rough kernels. Indiana Univ. Math. J. 47(2):455-469.

[8] Ying Yiming, 1999. A note on a class of singular integrals on product domains. Journal of Math. Study, 32(3): 264-271 (in Chinese with, Enghlish abstract).

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