- - - Department of Mathematics, Faculty of Science, University of Kurdistan, Pasdaran Ave., Postal Code: ۶۶۱۷۷-۱۷۵ Sanandaj, Iran.

In this paper, firstly, 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 v 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.

weighted spaces, holomorphic functions, de-la-Valle Poussion kernel, upper half-plane