RESEARCH ARTICLE

Marcinkiewicz integrals with rough kernels in H1Sn1

  • Daiqing ZHANG 1 ,
  • Feng LIU , 2
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  • 1. School of Computer Science and Mathematics, Fujian University of Technology, Fuzhou 350118, China
  • 2. Shandong University of Science and Technology, Qingdao 266590, China

Received date: 13 Oct 2020

Accepted date: 25 Jan 2021

Copyright

2021 Higher Education Press

Abstract

This paper is devoted to studying the Marcinkiewicz integral operators associated to polynomial compound curves. Some new bounds for the above operators on the Lebesgue, Triebel-Lizorkin, and Besov spaces are established by assuming that their rough kernels are given byΩH1Sn1 andhΔ+for someγ>1: It should be pointed out that the bounds are independent of h,Ω,γ and the coefficients of the polynomials in the definition of the operators.

Cite this article

Daiqing ZHANG , Feng LIU . Marcinkiewicz integrals with rough kernels in H1Sn1[J]. Frontiers of Mathematics in China, 2021 , 16(4) : 1163 -1189 . DOI: 10.1007/s11464-021-0913-x

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