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Boundary functions on a bounded balanced domain

Piotr Kot (2009)

Czechoslovak Mathematical Journal

We solve the following Dirichlet problem on the bounded balanced domain Ω with some additional properties: For p > 0 and a positive lower semi-continuous function u on Ω with u ( z ) = u ( λ z ) for | λ | = 1 , z Ω we construct a holomorphic function f 𝕆 ( Ω ) such that u ( z ) = 𝔻 z | f | p d 𝔏 𝔻 z 2 for z Ω , where 𝔻 = { λ | λ | < 1 } .

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