Weighted Fractional Differentiation Composition Operators from Mixed-Norm Spaces to Weighted-Type Spaces

Let be an open unit disc in the complex plane ℂ and let φ:→ as well as u:→ℂ be analytic maps. For an analytic functionf(z)=∑n=0∞anzn on the weighted fractional differentiation composition operator is defined as(Dφ,uβf)(z)=u(z)f[β](φ(z)), where β≥0,f[β](z)=∑n=0∞(Γ(n+1+β)/Γ(n+1))anzn, and f0z=fz. In this paper, we obtain a characterization of boundedness and compactness of weighted fractional differentiationcomposition operator from mixed-norm space Hp,q,ϕ to weighted-type space Hμ∞