Fractional Integrals on Product Manifolds |
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| Authors: | Yong Ding Xinfeng Wu |
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| Affiliation: | (1) School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems (BNU), Ministry of Education, Beijing Normal University, Beijing, 100875, The People’s Republic of China;(2) School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, The People’s Republic of China |
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| Abstract: | In this paper, the authors give a mixed norm estimate for the multi-parameter fractional integrals on product measurable spaces. This estimate is applied to obtain the boundedness for the fractional integrals of Nagel-Stein type on product manifolds, the fractional integral of Folland-Stein type with rough convolution kernels on product homogeneous groups, and the discrete fractional integrals of Stein-Wainger type. The research was supported by NSF of China (Grant: 10571015) and SRFDP of China (Grant: 20050027025). |
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| Keywords: | Multi-parameter fractional integral Mixed norm spaces Product manifolds Homogeneous group Discrete fractional integrals |
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