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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 $s \geqslant (N - 1)(1/p - 1/2)$, 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 $\bbfR^N \setminus \mathrm{supp}(f)$.

42B10Fourier type transforms, several variables
Full Text: DOI
[1] Alimov, Sh.; Ashurov, R.; Pulatov, A.: Multiple Fourier series and Fourier integrals, , 1-97 (1992) · Zbl 0782.42012
[2] Ahmedov, Anvarjon: The principle of general localization on unit sphere, J. math. Anal. appl. 356, No. 1, 310-321 (2009) · Zbl 1172.42012 · doi:10.1016/j.jmaa.2009.03.019
[3] Ashurov, R.: Summability almost everywhere of Fourier series in lp with respect to eigenfunctions, Mat. zametki 34, No. 6, 837-843 (1983) · Zbl 0536.42029 · doi:10.1007/BF01157406
[4] Bastys, A.: Generalized localization of Fourier series with respect to the eigenfunctions of the Laplace operator in the classes lp, Litovskii mat. Sb. 31, No. 3, 387-405 (1983) · Zbl 0799.35169 · doi:10.1007/BF00973052
[5] Carbery, A.; Soria, F.: Almost everywhere convergence of Fourier integrals for functions in Sobolev spaces, and an L2-localisation principle, Rev. mat. Iberoamericana 4, No. 2, 319-337 (1988) · Zbl 0692.42001
[6] Carbery, A.; Soria, F.: Pointwise Fourier inversion and localisation in rn, J. Fourier anal. Appl. 3, 847-858 (1997) · Zbl 0896.42007 · doi:10.1007/BF02656490
[7] Il’in, V.: On a generalized interpretation of the principle of localization for Fourier series with respect to fundamental systems of functions, Sibirsk. mat. Zh. 9, No. 5, 1093-1106 (1968) · Zbl 0191.07503
[8] Randol, B.: On the Fourier transform of the indicator function of a planar set, Trans. amer. Math. soc. 139, 271-279 (1969) · Zbl 0183.26904 · doi:10.2307/1995319
[9] Sjölin, P.: Regularity and integrability of spherical means, Monatsh. math. 96, No. 4, 277-291 (1983) · Zbl 0519.42018 · doi:10.1007/BF01471211
[10] Stein, E.; Weiss, G.: An introduction to Fourier analysis on Euclidean spaces, (1971) · Zbl 0232.42007
[11] Tao, T.: On the maximal Bochner-Bochner-Riesz conjecture in the plane for p<2, Trans. amer. Math. soc. 354, No. 5, 1947-1959 (2002) · Zbl 0992.42003