Inner functions in QK type spaces

Abstract

Inner functions in QK(p,q) are studied, provided K satisfies certain regularity conditions. In particular, it is shown that the only inner functions in QK(p,  p-2),   p≥1, are precisely the Blaschke products whose zeros {zn} satisfy sup⁡a∈D∑K(1-|φa(zn)|2)<∞.