Dergi makalesi Açık Erişim

Volterra operators between limits of Bergman-type weighted spaces of analytic functions

2021    Kizgut, Ersin

We characterize continuity and compactness of the Volterra integral operator T-g with the non-constant analytic symbol g between certain weighted Frechet or (LB)-spaces of analytic functions on the open unit disc, which arise as projective (resp. inductive) limits of intersections (resp. unions) of Bergman spaces of order 1 < p < infinity induced by the standard radial weight ( 1 - vertical bar z vertical bar(2))(alpha) for 0 < alpha < infinity. Motivated from the earlier results obtained for weighted Bergman spaces of standard weight, we also establish several results concerning the spectrum of the Volterra operators acting on the weighted Bergman Frechet space A(alpha+)(p), and acting on the weighted Bergman (LB)-space A(alpha-)(p).