Radial boundary values of Poisson integrals on infinite-dimensional balls (Q2634924)

The author considers the Gelfand triple \(E'\to H\to E\) associated with a separable Banach space \(E\) and constructs a unique right invariant measure \(\mu\) on its infinite-dimensional unitary group \(U(\infty)\). This measure is then used to define the infinite-dimensional Hardy spaces \({\mathcal H}_\mu^p\) on \(U(\infty)\), \(1\leq p\leq\infty\). Decompositions of this space into homogeneous components, integral formulae and directional derivatives are all investigated. In the final section, the author introduces a Poisson kernel \(P_r(u,v)\) for \(u,v\) in \(U(\infty)\) and \(0\leq r<1\) that allows the representation of values of functions in \({\mathcal H}_\mu^p\) via an integral formula.