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Two‐Point Projection Estimates for Harmonic Measure
Author(s) -
Betsakos Dimitrios
Publication year - 2003
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609303002108
Subject(s) - mathematics , harmonic measure , measure (data warehouse) , generalization , projection (relational algebra) , harmonic , harmonic function , mathematics subject classification , null set , set (abstract data type) , mathematical analysis , point (geometry) , unit disk , set function , pure mathematics , geometry , algorithm , physics , quantum mechanics , database , computer science , programming language
A theorem of Beurling and Nevanlinna gives a lower bound for the harmonic measure of a compact set in the unit disk in terms of the harmonic measure of a projection of the set. In this paper, a generalization of that result is proved, involving the sum of harmonic measures evaluated at two points. 2000 Mathematics Subject Classification 30C85, 31A15 (primary).