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\(L^p\) bounds for Marcinkiewicz integrals associated to homogeneous mappings

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Abstract

In this paper we study the \(L^p\)-mapping properties of Marcinkiewicz integral operators associated to homogeneous compound mappings. The kernels of our operators are allowed to be very rough both on the unit sphere and in the radial direction. We prove, among other things, that such operators are bounded on the Lebesgue spaces. The main results we obtain essentially improve and generalize some previous ones.

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Authors and Affiliations

  1. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590, People’s Republic of China

    Feng Liu

  2. School of Mathematical Sciences, Xiamen University, Xiamen, Fujian, 361005, People’s Republic of China

    Huoxiong Wu

Authors
  1. Feng Liu
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  2. Huoxiong Wu
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Corresponding author

Correspondence to Huoxiong Wu.

Additional information

Communicated by J. Escher.

The first author was supported by the NNSF of China (No. 11526122), Scientific Research Foundation of Shandong University of Science and Technology for Recruited Talents (No. 2015RCJJ053), Research Award Fund for Outstanding Young Scientists of Shandong Province (No. BS2015SF012) and Support Program for Outstanding Young Scientific and Technological Top-notch Talents of College of Mathematics and Systems Science (No. Sxy2016K01). The second author was supported by the NNSF of China (11371295, 11471041) and the NSF of Fujian Province of China (No. 2015J01025).

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Liu, F., Wu, H. \(L^p\) bounds for Marcinkiewicz integrals associated to homogeneous mappings. Monatsh Math 181, 875–906 (2016). https://doi.org/10.1007/s00605-016-0968-z

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  • DOI: https://doi.org/10.1007/s00605-016-0968-z

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