Czechoslovak Mathematical Journal, Vol. 67, No. 2, pp. 289-296, 2017


On Dyakonov type theorems for harmonic quasiregular mappings

Miloš Arsenović, Miroslav Pavlović

Received October 20, 2015.  First published March 1, 2017.

Abstract:  We prove two Dyakonov type theorems which relate the modulus of continuity of a function on the unit disc with the modulus of continuity of its absolute value. The methods we use are quite elementary, they cover the case of functions which are quasiregular and harmonic, briefly hqr, in the unit disc.
Keywords:  modulus of continuity; harmonic mapping; quasiregular mapping
Classification MSC:  30C62, 30C80
DOI:  10.21136/CMJ.2017.0562-15


References:
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[2] K. M. Dyakonov: Equivalent norms on Lipschitz-type spaces of holomorphic functions. Acta Math. 178 (1997), 143-167. DOI 10.1007/BF02392692 | MR 1459259 | Zbl 0898.30040
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[5] M. Pavlović: On K. M. Dyakonov's paper "Equivalent norms on Lipschitz-type spaces of holomorphic functions". Acta Math. 183 (1999), 141-143. DOI 10.1007/BF02392949 | MR 1719563 | Zbl 0989.46011
[6] M. Pavlović: Function Classes on the Unit Disc. An Introduction. De Gruyter Studies in Mathematics 52, De Gruyter, Berlin (2014). DOI 10.1515/9783110281903 | MR 3154590 | Zbl 1296.30002

Affiliations:   Miloš Arsenović, Miroslav Pavlović, University of Belgrade, Studentski trg 16, 11000 Belgrade, Serbia, e-mail: arsenovic@matf.bg.ac.rs, pavlovic@matf.bg.ac.rs

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