Differentiation operators and weighted composition operators on analytic function spaces

Weighted composition operators have been appearing in a natural way on 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. Recently, many mathematicians are attracted towards the study of weighted composition operators as it includes two nice classes of operators: namely composition operators and multiplication operators which have extensively been studied on different analytic function spaces. The differentiation operator is typically unbounded on many analytic function spaces. In our research project, we are planning to explore different properties ( e.g. boundedness, compactness, essential norm, differences ) of the products of weighted composition operators and differentiation operators between different Banach spaces of analytic functions.