Abstract. Szegő's theorem gives an explicit expression for the infinum of weighted $L^p$-norms over the circle for normalized analytic functions on the disc. The main result of the paper gives, in terms of the metrics on the Smirnov class $N^+$ and the classes $N^p$ $(1< p< \infty )$, the logarithmic version of Szegő's theorem.

AMS Subject Classification (1991): 30H05, 46J15

Received October 13, 1997. (Registered under 2648/2009.)