Abstract:Abstract. In this paper we introduce a class of increasing homeomorphic self-mappings of R. We define a harmonic extension of such functions to the upper halfplane by means of the Poisson integral. Our main results give some sufficient conditions for quasiconformality of the extension.1. Introduction. Let F be a complex-valued sense-preserving diffeomorphism of the upper halfplane C + := {z ∈ C : Im z > 0} onto itself, where C stands for the complex plane. Then the Jacobianis positive on C + and so the functio… Show more
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