Complex symmetry of multiplication and composition operators on A12(D)

Abstract For the set consisting of holomorphic functions over unit disk D whose derivativelies in the Bergman space A 2 (D) as well as in the classical Hardy space H 2 (D),we define a norm which is equivalent to the norm on the derivative Hardy space.We denote this space by A 1 2 (D). First, we’ll study some basic analytic propertiesof A 1 2 (D) and then obtain some characterizations of continuous multiplicationoperators on A 1 2 (D). In the last section, complex symmetries of composition operators on A 1 2 (D) with respect to a specific conjugation called standard conjugationare discussed. MSC2020: 47B33, 47B38