Fractional Volterra‐type operators from Bergman spaces to Hardy spaces

Abstract A new family of Volterra‐type operators based on bona fide fractional calculus is introduced in [12] by constructing analytic paraproducts acting on and their boundedness between Hardy spaces is characterized for certain parameter ranges there. This paper is a natural companion to [12] in the sense that it characterizes those ’s such that is bounded from weighted Bergman spaces to Hardy spaces for the range The case extends earlier results of Wu [32] and Miihkinen et al. [22]. Besides standard techniques in this area, the proof relies on certain recent results on fractional integration operators obtained in [14, 35].