AN EXTREMAL DECOMPOSITION PROBLEM FOR HARMONIC MEASURE

: Dubinin VN, Vuorinen M

Publisher: AMER MATHEMATICAL SOC

: 2012

: Proceedings of the American Mathematical Society

: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY

: P AM MATH SOC

: 7

: 140

: 7

: 2441

: 2446

: 6

: 0002-9939

DOI: https://doi.org/10.1090/S0002-9939-2011-11109-2

is greater than or equal to the harmonic measure omega(rho, E*, D*), where E* = {z : z(n) is an element of [-1,0]) and D* = {z : vertical bar z vertical bar < 1, vertical bar arg z vertical bar < pi/n}. This implies, for instance, a solution to a problem of R. W. Barnard, L. Cole, and A. Yu. Solynin concerning a lower estimate of the quantity inf (E) max(k=1), ..., (n) omega(a(k), E, D-k) for arbitrary points of the circle vertical bar z vertical bar = p. These authors stated this hypothesis in the particular case when the points are equally distributed on the circle vertical bar z vertical bar = rho.

Mathematics