(A) study on fejer-riesz inequality on the unit ball of Cn

Abstract

It has been proved by S. Power that the analogous Fejer-Riesz inequality also holds for the unit ball of $C^2$. In the present thesis, we extend this result to the higher dimensional unit ball. As related results we have the necessary and sufficient condition that the measure $d\mu=(1 - \mid{x}\mid^2)^\beta dA(\beta > -1)$ is a little Carleson measure on the unit ball.