Almost everywhere convergence of Cesàro means of Fourier series on the group of 2-adic integers |
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Authors: | Gy. Gát |
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Affiliation: | (1) Institute of Mathematics and Computer Science, College of Nyíregyháza, Nyíregyháza, P.O.Box 166., H-4400, Hungary |
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Abstract: | We prove the almost everywhere convergence of the Cesàro (C, α)-means of integrable functions σ n α f → f for f ∈ L 1(I), where I is the group of 2-adic integers for every α > 0. This theorem for the case of α = 1 was proved by the author [1]. For the case of the (C, 1) Fejér means there are several generalizations known with respect to some orthonormal systems. One could mention the papers [2, 9]. Research supported by the Hungarian National Foundation for Scientific Research (OTKA), grant no. T 048780. |
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Keywords: | character system group of 2-adic integers Fourier series Cesàro (C, α )-means a.e. convergence Hardy space |
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