Bull. Korean Math. Soc. 2022; 59(6): 1539-1555
Online first article September 6, 2022 Printed November 30, 2022
https://doi.org/10.4134/BKMS.b210874
Copyright © The Korean Mathematical Society.
Feng Liu, Yongming Wen, Xiao Zhang
Shandong University of Science and Technology; Minnan Normal University; Shandong University of Science and Technology
In this paper, we establish the boundedness and continuity for variation operators for $\theta$-type Calder\'{o}n--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: Variation operator, commutator, Triebel--Lizorkin space, boundedness and continuity
MSC numbers: Primary 42B20, 42B25
Supported by: 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).
2022; 59(6): 1471-1493
2021; 58(5): 1193-1208
2013; 50(6): 1923-1936
1999; 36(1): 139-146
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd