Quasi-Nearly Subharmonic Functions and Quasiconformal Mappings

被引：0
作者：
Pekka Koskela
Vesna Manojlović
机构：
[1] University of Jyväskylä,Department of Mathematics and Statistics
[2] University of Belgrade,Faculty of Organizational Sciences
来源：
Potential Analysis | 2012年 / 37卷
关键词：
Quasi-nearly subharmonic functions; Quasiconformal mappings; Regularly oscillating functions; 31C05; 30C65;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We prove that the composition of a quasi-nearly subharmonic function and a quasiregular mapping of bounded multiplicity is quasi-nearly subharmonic. Also, we prove that if u ∘ f is quasi-nearly subharmonic for all quasi-nearly subharmonic u and f satisfying some additional conditions, then f is quasiconformal. Similar results are further established for the class of regularly oscillating functions.
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页码：187 / 196
页数：9
相关论文
共 22 条
[1]  
Astala K(1983)A remark on quasiconformal mappings and BMO-functions Mich. Math. J. 30 209-212
[2]  
Cruz-Uribe D(2001)The minimal operator and the geometric maximal operator in Stud. Math. 144 1-37
[3]  
Dovgoshey O(2010)Bi-Lipschitz mappings and quasinearly subharmonic functions Int. J. Math. Math. Sci. 2010 1-8
[4]  
Riihentaus J(1972)-spaces of several variables Acta Math. 129 137-193
[5]  
Fefferman C(1931)Some properties of conjugate functions J. Reine Angew. Math. 167 405-423
[6]  
Stein EM(1995)Weighted Sobolev and Poincaré inequalities and quasiregular mappings of polynomial type Math. Scand. 77 251-271
[7]  
Hardy GH(1995)Definitions of quasiconformality Invent. Math. 120 61-79
[8]  
Littlewood JE(1992)-harmonic tensors and quasiregular mappings Ann. Math. 136 589-624
[9]  
Heinonen J(2007)Quasi-nearly subharmonic functions and conformal mappings Filomat (Niš) 21 243-249
[10]  
Koskela P(1974)Subharmonic behaviour of | J. Lond. Math. Soc. 8 529-538
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