ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 30D55, 46J15 Meštrović, Romeo, University of Montenegro, Yugoslavia Topologies on Some F -algebras of Holomorphic Functions For p > 1, the class N^{p} consists of all holomorphic functions f on the open unit disk in C for which

sup_{0≤r<1} ∫_{0}^{2π} (log^{+} |f(re^{iθ})|)^{p} \frac{dθ}{2π} < ∞.

By analogy with different topologies considered by J. E. McCarthy on the Smirnov class, we introduce and compare corresponding topologies on the space N^{p}. Further, we consider the individual spaces H^{2}(ω), where ω is a positive measurable function on the unit circle T such that ω and | log ω|^{p} are summable. We give asymptotic versions of Szegö’s and the Helson-Szegö theorem on these spaces, and characterize the universal multipliers of their duals.