Vol. 108, No. 2, 1983

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Factorization theorems for different classes of analytic functions in multiply connected domains

Dmitry Khavinson

Vol. 108 (1983), No. 2, 295–318

This paper consists of four sections. In the first section we give a survey on the reproducing kernel for harmonic functions in finitely-connected Jordan regions. We also prove a certain version of Fatou’s theorem which we will use in the next sections.

In the second part we construct the generalized Schwarz kernel for an arbitrary finitely-connected Jordan domain. This kernel reproduces any continuous single-valued analytic function inside the domain by the boundary values of its real part. Also, we give an explicit formula for the real part of this kernel in terms of the harmonic measures.

In the third section we study the Blaschke products in arbitrary Jordan domains.

The main results are contained in the fourth section. There we prove factorization theorems for the classes N, N+, Hp and Ep.

Mathematical Subject Classification 2000
Primary: 30C40
Secondary: 30D50, 30D55
Received: 30 May 1980
Revised: 22 November 1982
Published: 1 October 1983
Dmitry Khavinson
Mathematics and Statistics
University of South Florida
4202 E. Fowler Ave
Tampa FL 33620
United States