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

  • Feng Liu
  • Zunwei Fu
  • Seong Tae Jhang
Research Article


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.


Parametric Marcinkiewicz integral homogeneous mapping Triebel-Lizorkin space Besov space 


42B20 42B25 47G10 


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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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© Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.College of Mathematics and Systems ScienceShandong University of Science and TechnologyQingdaoChina
  2. 2.Department of MathematicsLinyi UniversityLinyiChina
  3. 3.School of Mathematical SciencesQufu Normal UniversityQufuChina
  4. 4.Department of Computer ScienceThe University of Suwon, Wau-ri, Bongdam-eup, Hwaseong-siGyeonggi-doKorea

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