Czechoslovak Mathematical Journal

, Volume 67, Issue 2, pp 289–296

On Dyakonov type theorems for harmonic quasiregular mappings



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.


modulus of continuity harmonic mapping quasiregular mapping 

MSC 2010

30C62 30C80 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [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.MathSciNetCrossRefMATHGoogle Scholar
  2. [2]
    K. M. Dyakonov: Equivalent norms on Lipschitz-type spaces of holomorphic functions. Acta Math. 178 (1997), 143–167.MathSciNetCrossRefMATHGoogle Scholar
  3. [3]
    K. M. Dyakonov: Holomorphic functions and quasiconformal mappings with smooth moduli. Adv. Math. 187 (2004), 146–172.MathSciNetCrossRefMATHGoogle Scholar
  4. [4]
    M. Mateljević: Distortions of quasiregular mappings and equivalent norms on Lipschitztype spaces. Abstr. Appl. Anal. 2014 (2014), Article ID 895074, 20 pages.Google Scholar
  5. [5]
    M. Pavlović: On K. M. Dyakonov’s paper “Equivalent norms on Lipschitz-type spaces of holomorphic functions”. Acta Math. 183 (1999), 141–143.MathSciNetCrossRefMATHGoogle Scholar
  6. [6]
    M. Pavlović: Function Classes on the Unit Disc. An Introduction. De Gruyter Studies in Mathematics 52, De Gruyter, Berlin, 2014.Google Scholar

Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2017

Authors and Affiliations

  1. 1.University of BelgradeBelgradeSerbia

Personalised recommendations