Corona problems in spaces of entire functions with growth conditions

Abstract

Let be the space of entire functions with growth conditions introduced by Hormander. If f…f m g belong to , let us consider the following condition: for some e, C > 0. In this paper we prove, for a weight function and for and for q⩾1, that (*) does not imply, in general, that g 2−1/q (when defined) belongs to the ideal generated in We also find two different kinds of conditions on an m-tuple under which, if f 1…,f m g satisfy (*), then g belongs to the ideal generated in