Mean oscillations and the convergence of Poisson integrals - Kolyada, V. I. (Ukrains’kyi Matematychnyi Zhurnal, 1997)
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.