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

摘要

Let𝔻be an open unit disc in the complex planeℂand letφ:𝔻→𝔻as well asu:𝔻→ℂbe analytic maps. For an analytic functionf(z)=∑n=0∞anznon𝔻the weighted fractional differentiation composition operator is defined as(Dφ,uβf)(z)=u(z)f[β](φ(z)), whereβ≥0,f[β](z)=∑n=0∞(Γ(n+1+β)/Γ(n+1))anzn, andf0z=fz. In this paper, we obtain a characterization of boundedness and compactness of weighted fractional differentiationcomposition operator from mixed-norm spaceHp,q,ϕto weighted-type spaceHμ∞.