Department of Mathematics, Faculty of Science, University of Kurdistan, Pasdaran Ave., Postal Code: 66177-175 Sanandaj, Iran.
In this paper, rstly, we obtain some inequalities which estimates complex polynomials on the circles.
Then, we use these estimates and a Moebius transformation to obtain the dual of this estimates for
the lines in upper half-plane. Finally, for an increasing weight on the upper half-plane with
certain properties and holomorphic functions f on the upper half-plane we obtain an equivalent
representation for weighted supremum norm.