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Failure of privalov's theorem on flatC2−εCurves in the Unit Ball ofC2

 

作者: S.M. Deckelman,  

 

期刊: Complex Variables, Theory and Application: An International Journal  （Taylor Available online 1996）
卷期: Volume 31, issue 4  

页码: 281-298

 

ISSN:0278-1077

 

年代: 1996

 

DOI:10.1080/17476939608814967

 

出版商: Gordon and Breach Science Publishers

 

关键词: Holomorphic function;modulus of absolute continuity;32A30;32A10;30A99

 

数据来源: Taylor

 

摘要:

In this paper we prove an extension of an estimate first proved by Ahern and Bruna of the modulus of absolute continuity holomorphic functions have on real analytic curves in the unit ball to a certain class of smooth curves satisfying a finite type condition. We then show that this yields insights into the sharpness of recent formulations of Privalov's theorem in the unit ball and in particular to the existence of counterexamples on flatC2−εcurves.

 

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