Essential Norm of Sum of Generalized Weighted Composition Operators between Weighted Spaces of Analytic Functions

Let (Formula presented.) be the open unit disc in the complex plane (Formula presented.) be the space of analytic functions on (Formula presented.) and (Formula presented.) be the set of analytic self-maps on (Formula presented.). Let (Formula presented.) be such that (Formula presented.) and (Formula presented.). We obtain estimates of the essential norms of the following sum of generalized weighted composition operators (Formula presented.) between weighted Banach spaces of analytic functions (Formula presented.) and (Formula presented.), which unifies the study of products of composition operators, multiplication operators and differentiation operators. As an application, we give the estimates of the essential norm of the operators (Formula presented.) and (Formula presented.). Also, we give the new characterizations of the estimates of the essential norms of the operators (Formula presented.) and (Formula presented.).