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Fractional Integrals on Product Manifolds

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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.

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Authors and Affiliations

  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

    Yong Ding

  2. School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, The People’s Republic of China

    Xinfeng Wu

Authors
  1. Yong Ding
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  2. Xinfeng Wu
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Corresponding author

Correspondence to Yong Ding.

Additional information

The research was supported by NSF of China (Grant: 10571015) and SRFDP of China (Grant: 20050027025).

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Ding, Y., Wu, X. Fractional Integrals on Product Manifolds. Potential Anal 30, 371–383 (2009). https://doi.org/10.1007/s11118-009-9120-1

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  • DOI: https://doi.org/10.1007/s11118-009-9120-1

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