Products of Differentiation Operators and Weighted Composition Operators between Weighted Bergman Spaces(Weighted Banach Spaces) and Weighted Zygmund-type Spaces( Weighted Bloch Spaces)

The product of two classes of operators: namely composition operators and multiplication operators gives rise to the class of weighted composition operators which have extensively been studied by many mathematicians and appearing in a natural way on different spaces of analytic functions. For instance, the isometries of Hardy spaces, Bergman spaces and many other Banach Spaces of analytic functions are weighted composition operators. Also, it is well known that the differentiation operator is typically unbounded on many analytic function spaces. In recent years, many mathematicians are attracted towards the study of product of differentiation operators and weighted composition operators on different spaces of analytic functions. In our proposed research project, our objective is to explore the properties of boundedness and compactness of the products of differentiation operators and weighted composition operators from weighted Bergman spaces to weighted Zygmund-type spaces and weighted Bloch spaces.