RESEARCH ARTICLE

Convergence of truncated rough singular integrals supported by subvarieties on Triebel-Lizorkin spaces

  • Feng LIU 1 ,
  • Qingying XUE , 2 ,
  • K^oz^o YABUTA 3
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  • 1. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China
  • 2. School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, China
  • 3. Research Center for Mathematical Sciences, Kwansei Gakuin University, Gakuen 2-1, Sanda 669-1337, Japan

Received date: 21 Mar 2018

Accepted date: 08 Apr 2019

Published date: 15 Jun 2019

Copyright

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

Abstract

Let be a function of homogeneous of degree zero and satisfy the cancellation condition on the unit sphere. Suppose that h is a radial function. Let Th,Ω,p be the classical singular Radon transform, and let Th,Ω,pε be its truncated operator with rough kernels associated to polynomial mapping p which is defined by Th,Ω,pεf(x)=||y|εf(xp(y))h(|y|)Ω(y)|y|ndy|. In this paper, we show that for any α(,) and (p,q) satisfying certain index condition, the operator Th,Ω,pε enjoys the following convergence properties limε0Th,Ω,pεfTh,Ω,pfF ˙αp,q(d)=0 and limε0Th,Ω,pεfTh,Ω,pfB ˙αp,q(d)=0 provided that ΩL(log+L)β(Sn1) for some β(0,1] or ΩH1(Sn1), or Ω(1qBq(0,0)(Sn1)).

Cite this article

Feng LIU , Qingying XUE , K^oz^o YABUTA . Convergence of truncated rough singular integrals supported by subvarieties on Triebel-Lizorkin spaces[J]. Frontiers of Mathematics in China, 2019 , 14(3) : 591 -604 . DOI: 10.1007/s11464-019-0765-9

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