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 \(s \geqslant (N - 1)(1/p - 1/2)\), then the Bochner-Riesz means of a function \(f \in L_p(\mathbb{R}^N), 1 \leqslant p \leqslant 2\) converge to zero almost-everywhere on \(\mathbb{R}^N \setminus \mathrm{supp}(f)\).


42B10 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
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