Type: Article
Publication Date: 1982-12-01
Citations: 101
DOI: https://doi.org/10.2140/pjm.1982.103.347
Let D={z: |2|<1} be the unit disk.Suppose ψ is an inner function with singular support K and let M L =H 2 QφH 2 where H 2 is the usual class of functions holomorphic on 2λ If μ is a positive measure on D, the closed disk, which assigns zero mass to K, then call μ a Carleson measure for M 1 if for a c>0, for all feM 1 .(Here and elsewhere, ||/|| 2 denotes the H 2 norm of an H 2 function.)In this paper the Carleson measures for M 1are characterized for all inner functions φ such that for some s, 0<ε<l, the set {z: \φ(z)\<ε} is connected.