About boundary values in

Author:
Piotr Kot

Journal:
Trans. Amer. Math. Soc. **363** (2011), 4063-4079

MSC (2010):
Primary 32A05, 32A40

DOI:
https://doi.org/10.1090/S0002-9947-2011-05083-X

Published electronically:
March 21, 2011

MathSciNet review:
2792980

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Abstract | References | Similar Articles | Additional Information

Abstract: Assume that is a balanced bounded domain with a holomorphic support function (e.g. strictly pseudoconvex domain with boundary). We denote . Let and be a circular invariant Borel probability measure on . If and is a continuous function on with on , then we construct nonconstant functions with , for and

Additionally if is a circular, bounded, strictly convex domain with boundary, then we give the construction of , the holomorphic function with: for all , where denotes the radial limit of . We also construct with for .

In all cases we can make arbitrarily small on a given compact subset and make it vanish to a given order at the point 0.

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Additional Information

**Piotr Kot**

Affiliation:
Instytut Matematyki, Politechnika Krakowska, ul. Warszawska 24, 31-155 Kraków, Poland

Email:
pkot@pk.edu.pl

DOI:
https://doi.org/10.1090/S0002-9947-2011-05083-X

Keywords:
Maximum modulus set,
inner function.

Received by editor(s):
December 16, 2007

Received by editor(s) in revised form:
April 13, 2009

Published electronically:
March 21, 2011

Article copyright:
© Copyright 2011
American Mathematical Society