Boundedness of Convolution Operators on Triebel - Lizorkin Spaces Via Fourier Transform Estimates

Authors

  • Xia Xia
  • Shanzhen Lu

Keywords:

convolution operator, Fourier transform estimates, singular integral operator, Triebel-Lizorkin space.

Abstract

In this paper, we study the boundedness of some convolution operators defined by Tf = ∑k∈Z σk*f on the homogeneous Triebel-Lizorkin spaces by Fourier transform estimates. As applications, we improve some known results, by proving the boundedness for singular integral operators with rough kernels on homogeneous Triebel-Lizorkin spaces. 

Key words and phrases. convolution operator, Fourier transform estimates, singular integral operator, Triebel-Lizorkin space.

2000 Mathematics Subject Classification. 42B20, 42B15

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Published

2025-05-18

How to Cite

Xia Xia, & Shanzhen Lu. (2025). Boundedness of Convolution Operators on Triebel - Lizorkin Spaces Via Fourier Transform Estimates. Jordan Journal of Mathematics and Statistics, 4(3), 201–218. Retrieved from https://jjms.yu.edu.jo/index.php/jjms/article/view/1149

Issue

Vol. 4 No. 3 (2011)

Section

Articles