Necessary and Sufficient Conditions for Inner Functions to Be in QK(p,p-2)‎-Spaces

Abstract EN

Under some regularity conditions on K, inner functions in QK(p,p-2)-spaces are characterized in the following way: an inner function belongs to QK(p,p-2) if and only if it is a Blaschke product associated with {zn} satisfying supa∈D∑nK(1-|φa(zn)|)<∞, where φa(z)=(a-z)/(1-a¯z).

The result generalizes earlier theorems in (Essén et al., 2006) and (Pérez-González and Rättyä, 2009).