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Zbl 1195.42053
Ashurov, Ravshan; Ahmedov, Anvarjon; Mahmud, Ahmad Rodzi B.
The generalized localization for multiple Fourier integrals.
(English)
[J] J. Math. Anal. Appl. 371, No. 2, 832-841 (2010). ISSN 0022-247X

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 $f \in L_p(\bbfR^N), 1 \leqslant p \leqslant 2$ converge to zero almost-everywhere on $\bbfR^N \setminus \mathrm{supp}(f)$.
[Włodzimierz Łenski (Poznań)]
MSC 2000:
*42B10 Fourier type transforms, several variables

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

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