Weighted hyperbolic composition groups on the disc and subordinated integral operators

We provide the spectral picture of groups of weighted composition operators, induced by the hyperbolic group of automorphisms of the unit disc, acting on holomorphic functions. Some questions about the spectrum of single weighted hyperbolic composition operators are discussed, and results related with them in the literature are completed or partly extended. Also, our results on the weighted hyperbolic group are applied to the spectral study of two families of multiparameter weighted averaging operators, which generalize both Siskakis' operator and the reduced Hilbert matrix operator.