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Zap. Nauchn. Sem. POMI, 2017, Volume 456, Pages 144–154 (Mi znsl6428)  

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

M. Ya. Mazalovab

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.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 1.3843.2017/4.6
НШ-9110.2016.1
Russian Foundation for Basic Research 16-01-00674


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English version:
Journal of Mathematical Sciences (New York), 2018, 234:3, 362–368

UDC: 517.575
Received: 25.05.2017

Citation: M. Ya. Mazalov, “On the existence of angular boundary values for polyharmonic functions in the unit ball”, Investigations on linear operators and function theory. Part 45, Zap. Nauchn. Sem. POMI, 456, POMI, St. Petersburg, 2017, 144–154; J. Math. Sci. (N. Y.), 234:3 (2018), 362–368

Citation in format AMSBIB
\Bibitem{Maz17}
\by M.~Ya.~Mazalov
\paper On the existence of angular boundary values for polyharmonic functions in the unit ball
\inbook Investigations on linear operators and function theory. Part~45
\serial Zap. Nauchn. Sem. POMI
\yr 2017
\vol 456
\pages 144--154
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6428}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2018
\vol 234
\issue 3
\pages 362--368
\crossref{https://doi.org/10.1007/s10958-018-4013-8}


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