Isometrical mappings between the szegö and the bergman-selberg spaces^∗

^∗Dedicated to Professor Nobuyuki Suita on his 60th birthday.

Abstract

Let Ω be a simply connected planar domain whose boundary is sufficiently smooth. Then some isometrical mappings between the Szegö and the Bergman-Selberg spaces on Ω are constructed, and they give the representations of the members in the Bergman-Selberg spaces in terms of members in the Szegö space. Moreover, for a member f in these analytic function spaces, some properties of the derivative ′ of f are examined.

AMS No:

• 30C40

^∗Dedicated to Professor Nobuyuki Suita on his 60th birthday.

^∗Dedicated to Professor Nobuyuki Suita on his 60th birthday.

Notes

^∗Dedicated to Professor Nobuyuki Suita on his 60th birthday.