Abstract. We derive a formula of a weight $v$ in terms of a given weight $w$ such that the estimate $$ \int_{\msbm D}| f(z)| ^pw(z) dm(z) \sim | f(0)| ^p + \int_{\msbm D}| f'(z)| ^pv(z) dm(z) $$ is valid for all analytic functions $f$ on the unit disc.

AMS Subject Classification (1991): 46E15, 30E99

Received February 15, 1999, and in revised form March 3, 2000. (Registered under 2758/2009.)