The generalized localization for multiple Fourier integrals. (English) Zbl 1195.42053

Ashurov, Ravshan; Ahmedov, Anvarjon; Mahmud, Ahmad Rodzi B.

J. Math. Anal. Appl. 371, No. 2, 832-841 (2010).

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 \(\mathbb{R}^N \setminus \mathrm{supp}(f)\).

Reviewer: Włodzimierz Łenski (Poznań)

MSC:

42B10

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

Keywords:

multiple Fourier integral; spectral expansions of elliptic differential operators; Bochner-Riesz means; the generalized localization

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