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On the mixed radial-angular integrability of Marcinkiewicz integrals with rough kernels

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Abstract

This paper studies the mixed radial-angular integrability of parametric Marcinkiewicz integrals along “polynomial curves”. Under the assumption that the kernels satisfy certain rather weak size conditions on the unit sphere with radial roughness, the authors prove that such operators are bounded on the mixed radial-angular spaces. Meanwhile, corresponding vector-valued versions are also obtained.

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Authors and Affiliations

  1. School of Mathematical Sciences, Xiamen University, Xiamen, 361005, China

    Ronghui Liu & Huoxiong Wu

  2. College of Mathematics and System Science, Shandong University of Science and Technology, Qingdao, 266590, China

    Feng Liu

Authors
  1. Ronghui Liu
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  2. Feng Liu
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  3. Huoxiong Wu
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Corresponding author

Correspondence to Huoxiong Wu.

Additional information

The authors were partly supported by the NSFC (11771358, 11701333, 11871101).

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Liu, R., Liu, F. & Wu, H. On the mixed radial-angular integrability of Marcinkiewicz integrals with rough kernels. Acta Math Sci 41, 241–256 (2021). https://doi.org/10.1007/s10473-021-0114-4

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  • DOI: https://doi.org/10.1007/s10473-021-0114-4

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