Zero Sets and Extensions of Bounded Holomorphic Functions in Polydiscs

P. S. Chee
1976 Proceedings of the American Mathematical Society  
A sufficient condition for a hypersurface in a polydisc U" to be the zero set of an HX(U") function is proved. This strengthens a result of Zarantonello and generalizes a result of Rudin. Using this result and a result of Andreotti and Stoll, a partial extension of Alexander's theorem on extension of bounded holomorphic functions from a hypersurface of U" to U" is obtained. Finally, a generalization of Cima's extension theorem for Hp functions is given.
doi:10.2307/2041122 fatcat:zy5ee3re3rh6rc7777gh5vd4xi