Bergman space methods and integral means spectra of univalent functions

Abstract: We study universal integral means spectra of certain classes of univalent functions defined on subsets of the complex plane. After reformulating the definition of the integral means spectrum of a univalent function in terms of membership in weighted Bergman spaces, we describe the Hilbert space techniques that can be used to estimate universal means spectra from above. Finally, we show that the method of norm expansion used in that context can be applied in a more general setting to reproducing kernel spaces in order to explicitly compute kernel functions.