On the possibility of holomorphic extension, into a domain, of functions defined on a connected piece of its boundary. II

This article is a continuation of [1] (see also [2]), in which simple criteria were obtained for the existence of holomorphic extension, into a domain, of a function defined on a connected piece of its boundary. The main result was obtained for the case when the domain is a “truncated” ball. Here we consider a wider class of domains and obtain corresponding criteria in explicit analytic form. For the case of a “truncated” ball these criteria are simpler than the ones in [1].