WEIGHTED COMPOSITION OPERATORS ON WEIGHTED SPACES OF ANALYTIC FUNCTIONS AND WEIGHTED SPACES OF CONTINUOUS FUNCTIONS

Weighted composition operators have been appearing in a natural way on different spaces of analytic functions and spaces of continuous functions. For instance, the isometries of Hardy spaces, Bergman spaces, many other Banach Spaces of analytic functions and spaces of continuous functions are weighted composition operators. This class of weighted composition operators is also important as it includes two classes of operators: namely composition operators and multiplication operators. For the last five decades the study of composition operators and multiplication have extensively been studied on different analytic function spaces and spaces of continuous functions. Recently, many mathematicians are attracted towards the study of weighted composition operators and their product with differentiation operator as it is well known that the differentiation operator is typical unbounded on many analytic function spaces. In ou r propsed research project, our objective is to explore boundedness, compactness, essential norm of the differences of weighted composition operators on weighted spaces of continuous functions. Also, these properties of boundedness, compactness, essential norm and their differences of product of weighted composition operators and differentiation operators on different spaces of analytic functions are to be explored.