A NOTE ON A TWO-PARAMETER FAMILY OF OPERATORS ${\MATHCAL A}^{B,C}$ ON WEIGHTED BERGMAN SPACES

Abstract

In this article, we prove that the two-parameter family of operators Ab,c is bounded on the weighted Bergman spaces B p α+c−1 if α + 2 < p and unbounded if α + 2 = p.

Keywords

• generalized ces´aro operator
• weighted bergman space
• boundedness