Quasiregular mappings and value distribution

AbstractWe define Hardy spaces $${\mathcal {H}}^p$$ H p for quasiregular mappings in the plane, and show that for a particular class of these mappings many of the classical properties that hold in the classical setting of analytic mappings still hold. This particular class of quasiregular mappings can be characterised in terms of composition operators when the symbol is quasiconformal. Relations between Carleson measures and Hardy spaces play an important role in the discussion. This program was initiated and developed for Hardy spaces of quasiconformal mappings by Astala and Koskela in 2011 in their paper $${\mathcal {H}}^p$$ H p -theory for Quasiconformal Mappings (Pure Appl Math Q 7(1):19–50, 2011).

Download Full-text

Moduli Space of Brody Curves, Energy and Mean Dimension

Nagoya Mathematical Journal ◽

10.1017/s0027763000025964 ◽

2008 ◽

Vol 192 ◽

pp. 27-58 ◽

Cited By ~ 10

Author(s):

Masaki Tsukamoto

Keyword(s):

Complex Plane ◽

Moduli Space ◽

Hermitian Manifold ◽

Value Distribution ◽

Holomorphic Map ◽

Infinite Dimensional ◽

Mean Dimension ◽

The Mean ◽

Moduli Theory ◽

Bounded Derivative

AbstractA Brody curve is a holomorphic map from the complex plane ℂ to a Hermitian manifold with bounded derivative. In this paper we study the value distribution of Brody curves from the viewpoint of moduli theory. The moduli space of Brody curves becomes infinite dimensional in general, and we study its “mean dimension”. We introduce the notion of “mean energy” and show that this can be used to estimate the mean dimension.

Download Full-text

On Properties of Differences Polynomials about Meromorphic Functions

Discrete Dynamics in Nature and Society ◽

10.1155/2012/569305 ◽

2012 ◽

Vol 2012 ◽

pp. 1-11

Author(s):

Jianming Qi ◽

Jie Ding ◽

Wenjun Yuan

Keyword(s):

Meromorphic Function ◽

Finite Order ◽

Special Class ◽

Meromorphic Functions ◽

Value Distribution ◽

Class Difference ◽

Difference Polynomial

We study the value distribution of a special class difference polynomial about finite order meromorphic function. Our methods of the proof are also different from ones in the previous results by Chen (2011), Liu and Laine (2010), and Liu and Yang (2009).

Download Full-text