Differences of differential operators between weighted-type spaces
Commun. Korean Math. Soc. Published online May 13, 2021
Mohammed Said Al-Ghafri and Jasbir Singh Manhas
Sultan Qaboos University
Abstract : Let H(D) be the space of analytic functions on the unit disc D. Let ψ=〖(ψ_j)〗_(j=0 )^n and Φ=〖(Φ_j)〗_(j=0 )^n be such that ψ_j, Φ_j ϵH(D). The linear differential operator is defined by T_ψ (f)=∑_(j=0)^n▒〖ψ_j f^((j)) 〗 , f ϵ H(D). We characterize the boundedness and compactness of the difference operator 〖(T〗_ψ-T_Φ)(f)=∑_(j=0)^n▒〖〖(ψ〗_j-Φ_j)f^((j)) 〗 between weighted-type spaces of analytic functions. As applications, we obtained boundedness and compactness of the difference of multiplication operators between weighted-type and Bloch-type spaces. Also, we give examples of unbounded (noncompact) differential operators such that their difference is bounded (compact).