Voitovych M. Asymptotic properties of subharmonic and analytic functions in the unit ball

The main fields of research in the PhD Thesis are: description of the asymptotic behavior of pth means of nonpositive M-subharmonic functions in the unit ball in terms of smoothness properties of the Riesz measure and boundary measure, description of the growth of the Cauchy-Stieltjes and Poisson-Stieltjes integral in the unit ball and description of the growth of spirallike functions in the unit disk. In PhD Thesis it is described the asymptotic behavior of pth means of the invariant Green potential in terms of smoothness properties of the measure. It is a generalization of the result due to M. Stoll. Also, based on previous results it is investigated the asymptotic behavior of M-subharmonic functions in the unit ball in terms of smoothness properties of the Riesz measure and the boundary measure. We are interested in description of the growth of analytic and harmonic functions in the unit ball represented by the Cauchy-Stieltjes or Poisson-Stieltjes integrals. We find estimates in terms of smoothness of the Stieltjes measure using the modulus of continuity of Stieltjes measure. It is described the maximum growth rate extremal spirallike functions. Also the Taylor coefficients of extremal function f are estimated.