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Mean oscillations and the convergence of Poisson integrals

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Abstract

We establish conditions for mean oscillations of a periodic summable function under which the summability of its Fourier series (conjugate series) by the Abel-Poisson method at a given point implies the convergence of Steklov means (the existence of the conjugate function) at the indicated point. Similar results are also obtained for the Poisson integral in ℝ n+1+ .

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Authors
  1. V. I. Kolyada
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Additional information

Odessa University, Odessa. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 2, pp. 206–222, February, 1997.

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Kolyada, V.I. Mean oscillations and the convergence of Poisson integrals. Ukr Math J 49, 227–246 (1997). https://doi.org/10.1007/BF02486438

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  • DOI: https://doi.org/10.1007/BF02486438

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