Bulletin of the Korean Mathematical Society (대한수학회보)

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BOUNDEDNESS AND CONTINUITY FOR VARIATION OPERATORS ON THE TRIEBEL-LIZORKIN SPACES

  • Feng, Liu (College of Mathematics and System Science Shandong University of Science and Technology) ;
  • Yongming, Wen (School of Mathematics and Statistics Minnan Normal University) ;
  • Xiao, Zhang (College of Electronic and Information Engineering Shandong University of Science and Technology)
  • Received : 2021.12.03
  • Accepted : 2022.03.04
  • Published : 2022.11.30
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Abstract

In this paper, we establish the boundedness and continuity for variation operators for θ-type Calderón-Zygmund singular integrals and their commutators on the Triebel-Lizorkin spaces. As applications, we obtain the corresponding results for the Hilbert transform, the Hermit Riesz transform, Riesz transforms and rough singular integrals as well as their commutators.

Keywords

Acknowledgement

The first author was partially supported by the National Natural Science Foundation of China (grant No. 11701333), the second author was partially supported by the Scientific Research Project of the Education Department of Fujian Province (No. JAT200331) and President's Fund of Minnan Normal University (No. KJ2020020).

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