Some classes of sets sufficient for holomorphic continuation of integrable functions

Bakhodir A. Shoimkhulov^a, Baymurat J. Kutlimuratov<sup>b

a</sup> National University of Uzbekistan, Tashkent, Uzbekistan
^b Karakalpak State University, Nukus, Uzbekistan

Abstract: In the present work we consider integrable functions defined on a boundary of a bounded domain $D$ in ${{\mathbb{C}}^{n}}$, $n>1$, and possessing a generalized Morera boundary property. We show that such functions possess a holomorphic continuation into the domain $D$ for some sufficient sets $\Gamma$ of complex lines.

Keywords: holomorphic continuation, Morera boundary condition, Bochner–Martinelli kernel.

UDC: 517.55

Received: 28.01.2024
Received in revised form: 02.03.2024
Accepted: 14.05.2024

Language: English