%0 Journal Article
%T Quasiconformal extension of meromorphic functions with nonzero pole
%A Bappaditya Bhowmik
%A Goutam Satpati
%A Toshiyuki Sugawa
%J Mathematics
%D 2015
%I arXiv
%X In this note, we consider meromorphic univalent functions $f(z)$ in the unit disc with a simple pole at $z=p\in(0,1)$ which have a $k$-quasiconformal extension to the extended complex plane $\hat{\mathbb C},$ where $0\leq k < 1$. We denote the class of such functions by $\Sigma_k(p)$. We first prove an area theorem for functions in this class. Next, we derive a sufficient condition for meromorphic functions in the unit disc with a simple pole at $z=p\in(0,1)$ to belong to the class $\Sigma_k(p)$. Finally, we give a convolution property for functions in the class $\Sigma_k(p)$.
%U http://arxiv.org/abs/1502.05125v1