Abstract
We consider a Gelfand triple $E'\rightarrow H\rightarrow E$ , so that E is a separable complex Banach space with dual $E'$ , and H is its dense Hilbert subspace. We investigate the problem of analytic extensions on an open ball $\mathcal{Q}\subset E'$ and their radial boundary values in the Hardy spaces $\mathcal{H}_{\mu}^{p}$ ( $1\le p\le\infty$ ) using the Poisson integrals on the unitary group $U(\infty)$ over H endowed with an invariant probability measure μ. For this purpose, we construct a Poisson-type kernel with the help of the symmetric Fock space Γ generated by H and prove that the set of radial boundary values of these analytic functions entirely coincides with $\mathcal{H}_{\mu}^{p}$ .
Highlights
1 Introduction A goal of the current work is to describe a certain type of complex-valued Poisson kernels generated by symmetric Fock spaces and associated Poisson integrals in the case of Hardy spaces in infinite-dimensional settings
This allows us to get a solution of the radial boundary problem for the corresponding analytic extensions
We consider a Gelfand triple E → H → E consisting of a separable complex Banach space E with dual E and a densely embedded Hilbert subspace H
Summary
A goal of the current work is to describe a certain type of complex-valued Poisson kernels generated by symmetric Fock spaces and associated Poisson integrals in the case of Hardy spaces in infinite-dimensional settings. The Hardy spaces Hμp ( ≤ p ≤ ∞) of Lpμ-integrable complex-valued functions are described in Section .
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