Frontiers of Mathematics in China >

2019 , Vol. 14 >Issue 1: 95 - 122

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

RESEARCH ARTICLE

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

  • Feng LIU 1 ,
  • Zunwei FU , 2,3 ,
  • Seong Tae JHANG 4
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  • 1. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China
  • 2. Department of Mathematics, Linyi University, Linyi 276005, China
  • 3. School of Mathematical Sciences, Qufu Normal University, Qufu 273100, China
  • 4. Department of Computer Science, The University of Suwon, Wau-ri, Bongdam-eup, Hwaseong-si, Gyeonggi-do, 445-743, Korea

Received date: 20 Oct 2018

Accepted date: 14 Dec 2018

Published date: 22 Mar 2019

Copyright

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

Key words： Parametric Marcinkiewicz integral; homogeneous mapping; Triebel-Lizorkin space; Besov space

Cite this article

Feng LIU , Zunwei FU , Seong Tae JHANG . Boundedness and continuity of Marcinkiewicz integrals associated to homogeneous mappings on Triebel-Lizorkin spaces[J]. Frontiers of Mathematics in China, 2019 , 14(1) : 95 -122 . DOI: 10.1007/s11464-019-0742-3

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