This article is cited in 59 papers

Analytic capacity: discrete approach and curvature of measure

M. S. Mel'nikov


Abstract: Certain discrete 'computable' quantities are introduced, and their interconnections and relations with analytic capacity are found out. The concept of curvature of a measure is introduced, which emerges naturally in the computations of the $L^2$-norm of the Cauchy transform of this measure. A lower bound on the analytic capacity, which uses the measure curvature and which has, to this extent, a geometric nature, is obtained.

UDC: 517.5

MSC: 30C85, 30E20

Received: 27.12.1994

 English version: Sbornik: Mathematics, 1995, 186:6, 827–846

Bibliographic databases:

• 
• 
•