Acta mathematica scientia,Series A ›› 2017, Vol. 37 ›› Issue (1): 38-53.

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Rough Marcinkiewicz Integrals Associated with Surfaces of Van der Corput Type

Liu Feng1, Xu Xiurong2, Zhang Jing3   

  1. 1. College of Mathematics and Systems Science, Shandong University of Science and Technology, Shandong Qingdao 266590;
    2. School of Mathematics and Statistics, Suzhou University, Anhui Suzhou 234000;
    3. School of Mathematics and Statistics, Yili Normal College, Xinjiang Yining 835000
  • Received:2016-07-09 Revised:2016-12-04 Online:2017-02-26 Published:2017-02-26
  • Supported by:

    Supported by the Natural Science Foundation of Xinjiang Province (2016D01C381)

Abstract:

This paper is concerned with the parametric Marcinkiewicz integrals with rough kernels associated with surfaces of Van der Corput type. Under the rather weakened size conditions on the integral kernels both on the unit sphere and in the radial direction, the Lp bounds of such operators are given in an extrapolation argument. Some previous results are greatly extended and improved.

Key words: Marcinkiewicz integrals, Rough kernels, Surfaces of Van der Corput type, Extrapolation

CLC Number: 

  • O174.3
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