On a modification of the Poisson integral operator
Dariusz Partyka (2011)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
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Given a quasisymmetric automorphism of the unit circle we define and study a modification of the classical Poisson integral operator in the case of the unit disk . The modification is done by means of the generalized Fourier coefficients of . For a Lebesgue’s integrable complexvalued function on , is a complex-valued harmonic function in and it coincides with the classical Poisson integral of provided is the identity mapping on . Our considerations are motivated by...