Weighted composition operators on Bicomplex bloch space

Abstract

Let U be the bidisk in BC and ϕ:U→U as well as f:U→U be a bicomplex holomorphic self map of U.For a bicomplex holomorphic map f on U the weighted composition operator u.C_ϕ is defined by u.(u.C_ϕ f)(z)=u(z).f o ϕ(z) for every z∈U,where ube a fixed bicomplex holomorphic function on U. The present study deals the condition for boundedness and compactness of Weighted Composition Operators on bicomplex Bloch space which define over the unit ball U, an extension of the classical Bloch space. The bicomplex Bloch is a higher-dimensional generalization of the Bloch space, structured to accommodate bicomplex analysis. The bicomplex Bloch space over the unit ball U is useful for studying more advanced problems in analysis.