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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
##### Keywords:
almost everywhere convergence; Bochner-Riesz means
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##### References:
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