| Title:
|
On Dyakonov type theorems for harmonic quasiregular mappings (English) |
| Author:
|
Arsenović, Miloš |
| Author:
|
Pavlović, Miroslav |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
67 |
| Issue:
|
2 |
| Year:
|
2017 |
| Pages:
|
289-296 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
modulus of continuity |
| Keyword:
|
harmonic mapping |
| Keyword:
|
quasiregular mapping |
| MSC:
|
30C62 |
| MSC:
|
30C80 |
| idZBL:
|
Zbl 06738519 |
| idMR:
|
MR3661041 |
| DOI:
|
10.21136/CMJ.2017.0562-15 |
| . |
| Date available:
|
2017-06-01T14:24:17Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146755 |
| . |
| Reference:
|
[1] Chen, S., Ponnusamy, S., Wang, X.: On planar harmonic Lipschitz and planar harmonic Hardy classes.Ann. Acad. Sci. Fenn., Math. 36 (2011), 567-576. Zbl 1279.30035, MR 2865514, 10.5186/aasfm.2011.3640 |
| Reference:
|
[2] Dyakonov, K. M.: Equivalent norms on Lipschitz-type spaces of holomorphic functions.Acta Math. 178 (1997), 143-167. Zbl 0898.30040, MR 1459259, 10.1007/BF02392692 |
| Reference:
|
[3] Dyakonov, K. M.: Holomorphic functions and quasiconformal mappings with smooth moduli.Adv. Math. 187 (2004), 146-172. Zbl 1056.30018, MR 2074174, 10.1016/j.aim.2003.08.008 |
| Reference:
|
[4] Mateljević, M.: Distortions of quasiregular mappings and equivalent norms on Lipschitz-type spaces.Abstr. Appl. Anal. 2014 (2014), Article ID 895074, 20 pages. MR 3273917, 10.1155/2014/895074 |
| Reference:
|
[5] Pavlović, M.: On K. M. Dyakonov's paper ``Equivalent norms on Lipschitz-type spaces of holomorphic functions''.Acta Math. 183 (1999), 141-143. Zbl 0989.46011, MR 1719563, 10.1007/BF02392949 |
| Reference:
|
[6] Pavlović, M.: Function Classes on the Unit Disc. An Introduction.De Gruyter Studies in Mathematics 52, De Gruyter, Berlin (2014). Zbl 1296.30002, MR 3154590, 10.1515/9783110281903 |
| . |
