Sums of Generalized Weighted Composition Operators Acting from Besov and BMOA Spaces to Bloch Spaces

This paper studies a generalized class of linear operators acting on spaces of analytic functions, defined by Pnψ,φ(f)(z)=∑j=0nψj(z)f(j)(φ(z)), where ψ={ψ0,ψ1,…,ψn}⊂H(D) and φ∈S(D). This formulation encompasses several classical operators, including composition, weighted composition, differentiation–composition, and the Stević–Sharma operator. We focus on the action of Pnψ,φ from BMOA and analytic Besov spaces Bp into the Bloch space B, and provide necessary and sufficient conditions for boundedness and compactness. These results unify and extend many previously known characterizations and demonstrate the flexibility of the Pnψ,φ framework in the context of analytic operator theory.