Weighted composition operators and differentiation operators between weighted banach spaces (weighted bergman spaces) and weighted zygmund-type spaces ( weighted bloch spaces)

The two classes of operators: namely composition operators and multiplication operators have extensively been studied on different analytic function spaces. The product of these two classes of operators gives rise to the class of weighted composition operators which have been 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. Recently, many mathematicians are attracted towards the study of weighted composition operators and differentiation operators. Also, it is well known that the differentiation operator is typically unbounded on many analytic function spaces. In our proposed research project, we are planning to explore boundedness, compactness, and essential norm of the products of weighted composition operators and differentiation operators from weighted Banach spaces of analytic functions and weighted Bergman spaces to weighted Zygmund-type spaces and weighted Bloch spaces.