2017
Том 69
№ 6

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Mean oscillations and the convergence of Poisson integrals

Kolyada V. I.

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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.

English version (Springer): Ukrainian Mathematical Journal 49 (1997), no. 2, pp 227-246.

Citation Example: Kolyada V. I. Mean oscillations and the convergence of Poisson integrals // Ukr. Mat. Zh. - 1997. - 49, № 2. - pp. 206–222.

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