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Regularity theorems for harmonic functions

Ganenkova E. G., Starkov V. V.

Journal of Applied Analysis

2015

Vol. 21, nr 1

25--36

The regularity theorem is a result stating that functions which have extremal growth or decrease in the given class display a regular behaviour. Such theorems for linearly invariant families of analytic functions are well known. We prove regularity theorems for some classes of harmonic functions. Many presented statements are new even in the analytic case.

Analytic in planar domains functions with preassigned asymptotic set

Ganenkova E. G, Starkov V. V

Journal of Applied Analysis

2014

Vol. 20, nr 1

7--14

In 1954 M. Heins proved that, for every analytic set A containing the infinity, there exists an entire function whose set of asymptotic values at the infinity equals A. We obtain analogs of this result for functions analytic in planar domains of arbitrary connectivity.