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Maximal operators and singular integrals with non-isotropic dilation on product domains

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Abstract

In this paper, the authors study the L p-mapping properties of certain maximal operators with non-isotropic dilation on product domains. As an application, the L p-boundedness of the corresponding non-isotropic multiple singular integral operator is also obtained. Here the integral kernel functions Ω belong to the spaces L(logL)α(Σ1 × Σ2) for some α > 0, which is optimal.

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Authors and Affiliations

  1. School of Mathematical Sciences, Capital Normal University, Beijing, 100037, P. R. China

    Zhong Kai Li

  2. College of Mathematics and Information Engineering, Jiaxing University, Jiaxing, 314001, P. R. China

    Bo Lin Ma

  3. School of Mathematical Sciences, Xiamen University, Xiamen, 361005, P. R. China

    Huo Xiong Wu

Authors
  1. Zhong Kai Li
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  2. Bo Lin Ma
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  3. Huo Xiong Wu
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Corresponding author

Correspondence to Huo Xiong Wu.

Additional information

Supported by National Natural Science Foundation of China (Grant Nos. 10771054, 10971141) and the NSF of Beijing (Grant No. 1092004)

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Li, Z.K., Ma, B.L. & Wu, H.X. Maximal operators and singular integrals with non-isotropic dilation on product domains. Acta. Math. Sin.-English Ser. 26, 1847–1864 (2010). https://doi.org/10.1007/s10114-010-8400-4

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  • DOI: https://doi.org/10.1007/s10114-010-8400-4

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