Subordination and 𝐻^{𝑝} functions

Abstract

Abstract.Let </> and W be inner functions with 0(0) = W(0) = 0. It is shown that if F is an exposed point of the unit ball of Hl and F(W(e"))/F(<j>(e"))>Q almost everywhere, then F o W = F o <fi . If / = zF such that F and \/F are in Hr and Hs, respectively, where \/r + \/s < 2 and 0 is a finite Blaschke product, then a necessary and sufficient condition is provided in order for f(W(e' ))/f(<f>(e' )) to be positive almost everywhere.