Title of the project The boundary of the unit ball in H^{1}. De rand van de eenheidsbal in H^{1}.

Abstract Let G be a bounded domain with smooth boundary in ℂ, an appropriate open Riemann surface, or a “good” domain in ℂ^{n}, (n > 1). The Hardy space H^{1} = H^{1}(G) consists of the holomorphic functions on G which have integrable boundary values. Thus H^{1} is a Banach space and a subspace of the L^{1}-space on the boundary of G. The unit ball of H^{1} has an interesting structure. Not all of the boundary points are extreme, and among the extreme points we can distinguish (non trivial) subclasses of exposed and strongly exposed points.

The purpose of the project is to advance our function theoretic understanding of these functional analytic properties of holomorphic functions.

We expect to use methods from function theory in one and several variables, but also ideas from operator theory and some harmonic analysis may enter.

Classification The project is in the range of the “werkgemeenschap analyse”. Mathematics subject classification: 30D55, 32A35, 46J15.