Frontiers of Mathematics in China >

2023 , Vol. 18 >Issue 2: 125 - 137

DOI: https://doi.org/10.3868/s140-DDD-023-0007-x

RESEARCH　ARTICLE

Boundedness of iterated spherical average

  • Rui BU 1 ,
  • Qiang HUANG , 2 ,
  • Yingjun SHAO 2
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  • 1. Department of Mathematics, Qingdao University of Science and Technology, Qingdao 266000, China
  • 2. Department of Mathematical Sciences, Zhejiang Normal University, Jinhua 321000, China
huangqiang0704@163.com

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2023 Higher Education Press 2023
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Abstract

The iterated spherical average Δ(A1)N is an important operator in harmonic analysis, and has very important applications in approximation theory and probability theory, where Δ is the Laplacian, A1 is the unit spherical average and (A1)N is its iteration. In this paper, we mainly study the sufficient and necessary conditions for the boundedness of this operator in Besov-Lipschitz space, and prove the boundedness of the operator in Triebel-Lizorkin space. Moreover, we use above conclusions to improve the existing results of the boundedness of this operator in Lp space.

Key words： Iterated spherical average; Besov-Lipschitz space; Triebel-Lizorkin space; $ L^{p} $ space

Cite this article

Rui BU , Qiang HUANG , Yingjun SHAO . Boundedness of iterated spherical average[J]. Frontiers of Mathematics in China, 2023 , 18(2) : 125 -137 . DOI: 10.3868/s140-DDD-023-0007-x

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