DIFFERENCES OF DIFFERENTIAL OPERATORS BETWEEN WEIGHTED-TYPE SPACES

Let H((Formula presented)) be the space of analytic functions on the unit disc (Formula presented). Let (Formula presented) and $ $ be such that (Formula presented) The linear differential operator is defined by (Formula presented) We characterize the boundedness and compactness of the difference operator (Formula presented) 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 (non compact) differential operators such that their difference is bounded (compact).