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.

Miloš Arsenović, Miroslav Pavlović, University of Belgrade, Studentski trg 16, 11000 Belgrade, Serbia, e-mail:,

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 2010): 30C62, 30C80

DOI: 10.21136/CMJ.2017.0562-15

Full text available as PDF.

  [1] S. Chen, S. Ponnusamy, X. Wang: On planar harmonic Lipschitz and planar harmonic Hardy classes. Ann. Acad. Sci. Fenn., Math. 36 (2011), 567-576. DOI 10.5186/aasfm.2011.3640 | MR 2865514 | Zbl 1279.30035
  [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
  [3] K. M. Dyakonov: Holomorphic functions and quasiconformal mappings with smooth moduli. Adv. Math. 187 (2004), 146-172. DOI 10.1016/j.aim.2003.08.008 | MR 2074174 | Zbl 1056.30018
  [4] M. Mateljević: Distortions of quasiregular mappings and equivalent norms on Lipschitz-type spaces. Abstr. Appl. Anal. 2014 (2014), Article ID 895074, 20 pages. DOI 10.1155/2014/895074 | MR 3273917
  [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

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