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The generalized localization for multiple Fourier integrals. (English) Zbl 1195.42053
Authors’ abstract: We investigate almost-everywhere convergence properties of the Bochner-Riesz means of $N$-fold Fourier integrals under summation over domains bounded by the level surfaces of the elliptic polynomials. It is proved that if the order of the Bochner-Riesz means $s⩾\left(N-1\right)\left(1/p-1/2\right)$, then the Bochner-Riesz means of a function $f\in {L}_{p}\left({ℝ}^{N}\right),1⩽p⩽2$ converge to zero almost-everywhere on ${ℝ}^{N}\setminus \mathrm{supp}\left(f\right)$.
##### MSC:
 42B10 Fourier type transforms, several variables
##### References:
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