ON WEIGHTED SPACES OF HARMONIC AND HOLOMORPHIC-FUNCTIONS

Weighed spaces of harmonic and holomorphic functions on the unit disc are studied. We show that for all radial weights which are not decreasing too fast the space of harmonic functions is isomorphic to c(0). For the weights that we consider we completely characterize those spaces of holomorphic functions which are isomorphic to c(0). Moreover, we determine when the Riesz projection, mapping the weighted space of harmonic functions onto the corresponding space of holomorphic functions, is bounded.