Inequalities for harmonic measures with respect to non-overlapping domains. (October 2015)

• Record Type: Journal Article
• Authors: Dubinin, V. N.
• Is Part Of: Izvestiya. Volume 79:Number 5(2015)
• Page Start: 902
• Page End: 918
• Publication Date: 2015-10
• Subjects: 30C85 -- 31A15 -- 30C75; harmonic measure -- condenser capacity -- logarithmic capacity -- Schwarzian derivative.; Mathematics -- Periodicals; 510.5
• DOI: 10.1070/IM2015v079n05ABEH002766
• Languages: English
• ISSNs: 1064-5632

Abstract

Abstract: Let and be the components of the complement of a closed Jordan curve, and let, where . We extend the known inequality for the harmonic measures of with respect to and to the case of an arbitrary number of pairwise non- overlapping domains, , and prove analogous inequalities for the harmonic measures of sets concentrated in several discs or continua, , of a given logarithmic capacity. We also establish bounds for these measures in terms of the Schwarzian derivatives of functions that conformally map the domains onto the unit disc.