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Boundary functions in L 2 H ( 𝔹 n )

Piotr Kot (2007)

Czechoslovak Mathematical Journal

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 𝔹 n we give necessary and sufficient conditions in order that there exists a holomorphic function f 𝕆 ( 𝔹 n ) such that u ( z ) = | λ | < 1 f ( λ z ) 2 d 𝔏 2 ( λ ) .

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