On almost everywhere convergence of Bochner-Riesz means in higher dimensions. (English) Zbl 0569.42011
In \({\mathbb{R}}^ n\) define \((T_{\lambda,r}f){\hat{\;}}(\xi)=\hat f(\xi)(1-| r^{-1}\xi^ 2|)_+^{\lambda}.\) If \(n\geq 3\), \(\lambda >1/2(n-1)/(n+1)\) and \(2\leq p<2n/(n-1-2\lambda),\) then \(\lim_{r\to \infty}T_{\lambda,r}f(x)=f(x)\) a.e. for all \(f\in L^ p({\mathbb{R}}^ n).\)
MSC:
| 42B10 | Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type |
References:
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