Toeplitz-Superposition Operators on Analytic Bloch Spaces

The important purpose of this current work is to study a new class of operators, the so-called Toeplitz-superposition operators as an expansion of the weighted known composition operators, induced by such continuous entire functions mapping on bounded specific sets. Minutely, we have deeply discussed the conditions for boundedness of this new type of operators between certain types of some holomorphic Bloch classes with some specific values of the weighted functions.

Bicomplex Bergman and Bloch spaces

In this article, we define the bicomplex weighted Bergman spaces on the bidisk and their associated weighted Bergman projections, where the respective Bergman kernels are determined. We study also the bicomplex Bergman projection onto the bicomplex Bloch space.