Integral means spectrum functionals on Teichmuller spaces

In this paper we introduce and study the integral means spectrum (IMS) functionals on Teichmüller spaces. We show that the IMS functionals on the closure of the universal Teichmüller space and the universal asymptotic Teichmüller space are both continuous. During the proof, we consider the Pre-Schwarzian derivative model of universal asymptotic Teichmüller space and establish some new results for it. We also show that the integral means spectrum of any univalent function admitting a quasiconformal extension to the extended complex plane is strictly less than the universal integral means spectrum.