Boundedness of iterated spherical average

doi:10.3868/s140-DDD-023-0007-x

Front. Math. China

2023, Vol. 18

Issue (2) : 125-137 https://doi.org/10.3868/s140-DDD-023-0007-x

RESEARCH　ARTICLE

Boundedness of iterated spherical average

Rui BU¹, Qiang HUANG²(

), Yingjun SHAO²

¹. Department of Mathematics, Qingdao University of Science and Technology, Qingdao 266000, China
². Department of Mathematical Sciences, Zhejiang Normal University, Jinhua 321000, China

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Abstract

The iterated spherical average $Δ (A 1) N$ is an important operator in harmonic analysis, and has very important applications in approximation theory and probability theory, where $Δ$ is the Laplacian, $A 1$ is the unit spherical average and $(A 1) N$ 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 $L p$ space.

Keywords Iterated spherical average Besov-Lipschitz space Triebel-Lizorkin space $ L^{p} $ space

Corresponding Author(s): Qiang HUANG

About author:

Peng Lei and Charity Ngina Mwangi contributed equally to this work.

Online First Date: 19 October 2023 Issue Date: 13 November 2023

Cite this article:

Rui BU,Qiang HUANG,Yingjun SHAO. Boundedness of iterated spherical average[J]. Front. Math. China, 2023, 18(2): 125-137.

URL:

https://academic.hep.com.cn/fmc/EN/10.3868/s140-DDD-023-0007-x
https://academic.hep.com.cn/fmc/EN/Y2023/V18/I2/125

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