Stevic-Sharma Operator on Spaces of Vector-Valued Holomorphic Functions

In this paper, we are interested in the Stevic-Sharma operator on the spaces of vector-valued holomorphic functions, which has never been considered so far. We completely characterize the boundedness of the Stevic-Sharma operator between weak and strong vector-valued Bergman spaces in terms of a Julia-Caratheodory type function theoretic characterization and a power type characterization. Furthermore, we establish an interesting result: the boundedness of the Stevic-Sharma operator between weak and strong vector-valued Bergman spaces is not only equivalent to the Hilbert-Schmidtness but also equivalent to the order boundedness of the Stevic-Sharma operator between scalar value Bergman spaces.