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Boundary functions in L 2 H \((\mathbb{B}^n )\)

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Abstract

We solve the Dirichlet problem for line integrals of holomorphic functions in the unit ball

For a function u which is lower semi-continuous on \(\partial \mathbb{B}^n \) we give necessary and sufficient conditions in order that there exists a holomorphic function f ∈ \(\mathbb{O}(\mathbb{B}^n )\) such that

$$u(z) = \int_{\left| \lambda \right| < 1} {\left| {f(\lambda z)} \right|^2 d\mathfrak{L}^2 (\lambda )} .$$

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Authors and Affiliations

  1. Instytut Matematyki, Politechnika Krakowska, ul.Warszawska 24, 31-155, Kraków, Poland

    Piotr Kot

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  1. Piotr Kot
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Kot, P. Boundary functions in L 2 H \((\mathbb{B}^n )\) . Czech Math J 57, 29–47 (2007). https://doi.org/10.1007/s10587-007-0041-0

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  • DOI: https://doi.org/10.1007/s10587-007-0041-0

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