Improving multipliers and zero sets in QK spaces

Abstract

Let X and Y be two spaces of analytic functions in the unit disk D with (Formula Presented.). An inner function θ is said to be (X, Y)-improving if (Formula Presented.) whenever (Formula Presented.) and (Formula Presented.). Under mild conditions on the weight function K, we prove that inner functions in QK are precisely the ones which are (QK, BMOA)-improving and (QK, B)-improving. Meanwhile, the zero sets in QK spaces are determined in terms of Carleson–Newman sequences.