An equivalent representation for weighted supremum norm on the upper half-plane

Abstract

In this paper, rstly, we obtain some inequalities which estimates complex polynomials on the circles.<br />Then, we use these estimates and a Moebius transformation to obtain the dual of this estimates for<br />the lines in upper half-plane. Finally, for an increasing weight on the upper half-plane with<br />certain properties and holomorphic functions f on the upper half-plane we obtain an equivalent<br />representation for weighted supremum norm.