Melih ERYİǦİT, Sinem SEZER, Simten BAYRAKÇI

On the convergence of the Abel–Poisson means of multiple Fourier series

Let Aε(x, f) be the Abel–Poisson means of an integrable function f(x) on n–dimensional torus $T^n$ , −π < xi ≤ π, i = 1, . . . , n (n ≥ 2) in the Euclidean n–space. The famous Bochner’s theorem asserts that for any function f ∈ L 1 (T n ) the Abel–Poisson means Aε(x, f) are pointwise converge to f(x) a.e., that is, lim ε→0+ Aε(x, f) = f(x), a.e. x ∈ $T^n$ . In this paper we investigate the rate of convergence of Abel–Poisson means at the so-called µ–smoothness point of f .

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