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Boundedness and continuity of Marcinkiewicz integrals associated to homogeneous mappings on Triebel-Lizorkin spaces

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Abstract

We establish the boundedness and continuity of parametric Marcinkiewicz integrals associated to homogeneous compound mappings on Triebel-Lizorkin spaces and Besov spaces. Here the integral kernels are provided with some rather weak size conditions on the unit sphere and in the radial direction. Some known results are naturally improved and extended to the rough case.

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Acknowledgements

This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 11701333, 11671185, 11771195) and the Support Program for Outstanding Young Scientific and Technological Top-notch Talents of College of Mathematics and Systems Science (Grant No. Sxy2016K01).

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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. Department of Mathematics, Linyi University, Linyi, 276005, China

    Zunwei Fu

  3. School of Mathematical Sciences, Qufu Normal University, Qufu, 273100, China

    Zunwei Fu

  4. Department of Computer Science, The University of Suwon, Wau-ri, Bongdam-eup, Hwaseong-si, Gyeonggi-do, 445-743, Korea

    Seong Tae Jhang

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  1. Feng Liu
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  2. Zunwei Fu
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  3. Seong Tae Jhang
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Correspondence to Zunwei Fu.

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Liu, F., Fu, Z. & Jhang, S.T. Boundedness and continuity of Marcinkiewicz integrals associated to homogeneous mappings on Triebel-Lizorkin spaces. Front. Math. China 14, 95–122 (2019). https://doi.org/10.1007/s11464-019-0742-3

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  • DOI: https://doi.org/10.1007/s11464-019-0742-3

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