On the Convergence of Bochner-Riesz's Spherical Means of Fourier Double Integrals
Keywords:Double integrals, spherical means, convergence
AbstractIn this paper we consider the convergence by measure of Fourier integral spherical means of Riesz at a critical exponent Î´ = 1/2 after changing the values of the integrable function on the given set of a small measure.
S. Bochner, Summation of multiple Fourier series by spherical means, Trans. Amer. Math. Soc., 40 (1936), 175–207.
B. I. Golubov, On the convergence of Riesz spherical means of multiple Fourier series and integrals of functions of bounded generalized variation, Mat. Sb., 89(131) (1972), 630–653; English transl. Math. USSR Sb., 18 (1972).
B. I. Golubov, The summability of conjugate multiple Fourier integrals by Riesz means, Uspehi Mat. Nauk, 31no. 5(191) (1976), 237–238, (in Russian).
M. G. Grigorian, Uniform convergence of the greedy algorithm with respect to the Walsh system, Studia Math., 198(2) (2010), 197–206.
M. G. Grigorian, On the Lp-strong property of orthonormal systems, Math. Sb. 194:10, 77–106 (in Russ.), English transl. Sbornik: Math. 194:10 (2003), 1503–1532.
M. G. Grigorian, On the convergence of Fourier series in the metric of L1, Analysis Math., (1991), 17(3), 211–237.
M. G. Grigoryan and L. N. Galoyan, On the uniform convergence of negative order Cesaro means of Fourier series, J. Math. Anal. Appl., 434 (1) (2016), 554–567.
M. G. Grigoryan, and A. A. Sargsyan, On the universal functions for the class Lp[0, 1], J. Functional Analysis, 270 (2016), 3111–3133.
M. G. Grigoryan, Modifications of functions, Fourier coefficients and nonlinear approximation, Matem. Sb., 203 (3) (2012), 49–78.
N. N. Luzin, On the fundamental theorem of the integral calculus, Mat. Sb. 28 (1912), 266–294 (in Russian).
D. E. Men‘shov, Sur la convergence uniforme des series de Fourier, Mat. Sb. 11(53) (1942), 67–96, (French-Russian summary).
E. M. Stein, On limits of sequences of operators, Ann. of Math., 74 (1961), 140–170.
E. M. Stein and G. Weiss, Introduction to Fourier analysis on Euclidean Spaces, Princeton University Press, PMS Vol. 32, 1971.