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Boundedness and continuity of maximal singular integrals and maximal functions on Triebel-Lizorkin spaces

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Abstract

In this paper, we systematically study several classes of maximal singular integrals and maximal functions with rough kernels in \(\mathscr{F}_{\beta}\left(\mathrm{S}^{n-1}\right)\), a topic that relates to the Grafakos-Stefanov class. The boundedness and continuity of these operators on Triebel-Lizorkin spaces and Besov spaces are discussed.

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Acknowledgements

The first author was supported by National Natural Science Foundation of China (Grant No. 11701333) and Support Program for Outstanding Young Scientific and Technological Top-Notch Talents of College of Mathematics and Systems Science (Grant No. Sxy2016K01). The second author was supported by National Natural Science Foundation of China (Grant Nos. 11471041 and 11671039) and National Natural Science Foundation of China-Deutsche Forschungsgemeinschaft (Grant No. 11761131002). The third author was supported by Grant-in-Aid for Scientific Research (C) (Grant No. 15K04942), Japan Society for the Promotion of Science. The authors express their sincere gratitude to the referees for their helpful remarks and suggestions, which made this paper more readable.

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Authors and Affiliations

  1. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590, China

    Feng Liu

  2. Laboratory of Mathematics and Complex Systems (Ministry of Education of China), School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China

    Qingying Xue

  3. Research Center for Mathematical Science, Kwansei Gakuin University, Sanda, 669-1337, Japan

    Kôzô Yabuta

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  1. Feng Liu
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  2. Qingying Xue
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  3. Kôzô Yabuta
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Correspondence to Feng Liu.

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Liu, F., Xue, Q. & Yabuta, K. Boundedness and continuity of maximal singular integrals and maximal functions on Triebel-Lizorkin spaces. Sci. China Math. 63, 907–936 (2020). https://doi.org/10.1007/s11425-017-9416-5

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  • DOI: https://doi.org/10.1007/s11425-017-9416-5

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