Certain Invariant Spaces of Bounded Measurable Functions on a Sphere

Abstract

In their 1976 paper, Nagel and Rudin characterize the closed unitarily and Möbius invariant spaces of continuous and $L^p$-functions on a sphere, for $1\le p<\infty$. In this paper we provide an analogous characterization for the weak*-closed unitarily and Möbius invariant spaces of $L^{\infty }$-functions on a sphere. We also investigate the weak*-closed unitarily and Möbius invariant algebras of $L^{\infty }$-functions on a sphere.

16 pages, submitted for publication