M. Ya. Mazalov, “On the existence of angular boundary values for polyharmonic functions in the unit ball”, Zap. Nauchn. Sem. POMI, 2017, Volume 456,Pages <nobr>144

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On the existence of angular boundary values for polyharmonic functions in the unit ball

M. Ya. Mazalov^ab

^a National Research University "Moscow Power Engineering Institute" in Smolensk, Smolensk, Russia
^b Bauman Moscow State Technical University, Moscow, Russia

Abstract: We study boundary properties of polyharmonic functions. In particular, a criterion is obtained (in terms of the radial growth of th derivative) for the existence a.e. of angular boundary values for a polyharmonic function bounded in the unit ball.

Key words and phrases: polyharmonic functions, polyanalytic functions, boundary properties, Poisson integral, lacunary series.

UDC: 517.575

Received: 25.05.2017