On holomorphic continuation of integrable functions along finite families of complex lines in an $n$-circular domain

Bayram P. Otemuratov

Karakalpak State University, Nukus, 230112, Uzbekistan

Abstract: This paper contains some results related to holomorphic extension of integrable functions defined on the boundary of $D\subset\mathbb C^n$, $n>1$ into this domain. We shall consider integrable functions with the property of holomorphic extension along complex lines. In the complex plane $\mathbb C$ the results about functions with such property are trivial. Therefore, our results are essentially multidimensional.

Keywords: integrable functions, holomorphic extension, Szegö kernel, Poisson kernel, complex lines.

UDC: 517.55

Received: 06.07.2017
Received in revised form: 16.08.2017
Accepted: 30.11.2017

Language: English

DOI: 10.17516/1997-1397-2018-11-1-91-96

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