turkmath.org

It is very well known that every composition operator on Hardy spaces of the unit disc is bounded whereas the boundedness of composition operators on Hardy spaces of the half-plane is not always possible. In 1999 Matache characterized the boundedness of composition operators of the half-plane in terms of Carleson measures. In 2012 M. Jury and S. Elliott, using the theory of positive kernels, found a geometrical criterion in terms of the derivative of the inducing function at infinity for the boundedness of composition operators of the half-plane. In this talk we will survey the result of Jury and Elliott. I will give a brief introduction to the theory of positive kernels. We will also discuss the posibility of extending the method of Jury and Elliott to Hardy spaces of the poly-disc.