BOCHNER–RIESZ MEANS ON BLOCK-SOBOLEV SPACES IN COMPACT LIE GROUP
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Published:2020-01-08
Issue:2
Volume:109
Page:176-192
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ISSN:1446-7887
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Container-title:Journal of the Australian Mathematical Society
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language:en
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Short-container-title:J. Aust. Math. Soc.
Author:
CHEN JIECHENG,FAN DASHAN,ZHAO FAYOU
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 $\mathbb{T}^{m}$.
Publisher
Cambridge University Press (CUP)
Subject
General Mathematics
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