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.
@article{bwmeta1.element.doi-10_2478_v10062-008-0011-5,
author = {Andrzej Michalski},
title = {Sufficient conditions for quasiconformality of harmonic mappings of the upper halfplane onto itself},
journal = {Annales UMCS, Mathematica},
volume = {62},
year = {2008},
pages = {91-104},
zbl = {1179.30016},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10062-008-0011-5}
}
Andrzej Michalski. Sufficient conditions for quasiconformality of harmonic mappings of the upper halfplane onto itself. Annales UMCS, Mathematica, Tome 62 (2008) pp. 91-104. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10062-008-0011-5/
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