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BOCHNER–RIESZ MEANS ON BLOCK-SOBOLEV SPACES IN COMPACT LIE GROUP
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 109 / Issue 2 / October 2020
- Published online by Cambridge University Press:
- 08 January 2020, pp. 176-192
- Print publication:
- October 2020
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- Article
- Export citation
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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 
$\mathbb{T}^{m}$.
