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BOCHNER–RIESZ MEANS ON BLOCK-SOBOLEV SPACES IN COMPACT LIE GROUP

Part of: Abstract harmonic analysis Harmonic analysis in several variables

Published online by Cambridge University Press:  08 January 2020

JIECHENG CHEN ,
DASHAN FAN  and
FAYOU ZHAO
JIECHENG CHEN
Affiliation:
Department of Mathematics,Zhejiang Normal University, Jinhua 321000, PR China email jcchen@zjnu.edu.cn
DASHAN FAN
Affiliation:
Department of Mathematical Sciences,University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA Department of Mathematics,Zhejiang Normal University, Jinhua 321000, PR China email fan@uwm.edu
FAYOU ZHAO*
Affiliation:
Department of Mathematics,Shanghai University, Shanghai 200444, PR China email fyzhao@shu.edu.cn
*
✉fyzhao@shu.edu.cn
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Abstract

On a compact Lie group $G$ of dimension $n$, we study the Bochner–Riesz mean $S_{R}^{\unicode[STIX]{x1D6FC}}(f)$ of the Fourier series for a function $f$. At the critical index $\unicode[STIX]{x1D6FC}=(n-1)/2$, we obtain the convergence rate for $S_{R}^{(n-1)/2}(f)$ when $f$ is a function in the block-Sobolev space. The main theorems extend some known results on the $m$-torus $\mathbb{T}^{m}$.

Keywords

Bochner–Riesz meansblock spaceblock-Sobolev spacecompact Lie groupsFourier seriesmaximal operatoralmost everywhere convergence

MSC classification

Primary: 43A22: Homomorphisms and multipliers of function spaces on groups, semigroups, etc. 43A32: Other transforms and operators of Fourier type
Secondary: 42B25: Maximal functions, Littlewood-Paley theory 42B35: Function spaces arising in harmonic analysis
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 109 , Issue 2 , October 2020 , pp. 176 - 192
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Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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Footnotes

The research was supported by National Natural Science Foundation of China (grant nos. 11671363, 11871436, 11871108, 11971295) and Natural Science Foundation of Shanghai (no. 19ZR1417600).

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