Integral mean of Green’s potentials and their conjugate

Ya. V. Vasyl'kiv, M. Ya. Kravec

Abstract


The best possible estimates for Lebesgue integral means $m_q(r,F)\; (1\le q<+\infty)$ for the pair of functions $F= g+i\:\breve{g}$, here $g$ - Green's potential, $\breve{g}$ - function conjugate to $g$, was obtained. It generalizes well-known results of Ya.V. Vasyl'kiv and A.A. Kondratyuk for logarithms $\log\; B$ of Blaschke products $B$ in terms of counting function $n(r,0,B)\; (0<r<1)$ of their zeroes.

Keywords


Green's potentials, conjugate function, Lebesgue integral means, distribution of values of subharmonic functions

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