INTERPOLATING SEQUENCES FOR A~∞(φ)-FUNCTIONS

摘要

Let φ be a normal function on [0, 1) and A~∞(φ) of functions f analytic on the unit disk D={z: |z|1} with sup {φ(|z|)|f(z)|: z∈D}∞. A sequence {z_n}(?)D defines an operator T from A~∞(φ) to l~∞ by Tf=(φ(|z_n|)f(z_n)}for f∈A~∞. A necessary and sufficient condition for TA~∞(φ)=l~∞ is given by inf