Essential norm of intrinsic operators from Banach spaces of analytic functions into weighted-type spaces

In this work, we characterize the boundedness of a large class of operators, mapping a general Banach space of analytic functions defined on the open unit disk into a weighted-type Banach space of analytic functions and obtain estimates on the essential norm. The results show that the boundedness of such operators depends only on the behavior of the kernel functions. The results we obtain are extensions of previous work dealing with several specific classes of operators: the multiplication operator, the composition operator, the weighted composition operator, and a certain integral operator. We present applications to various choices of the domain space X, including the Hardy space H-P, the space S-P consisting of the functions whose derivatives are in H-P, the Bloch-type spaces B-a (for a = 1), BMOA, and the weighted Bergman space A(a)(P) (for P = 1, a > -1).