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EMBEDDING DERIVATIVES OF FOCK SPACES AND GENERALIZED WEIGHTED COMPOSITION OPERATORS

. In this paper, we give complete characterizations of those positive Borel measures such that the differentiation operator D ( n ) f = f ( n ) is bounded or compact from Fock spaces F p ( C ) into a class weighted Lebesgue spaces on complex plane C . As an application, we characterize the boundedness and compactness of generalized weighted composition operators acting on Fock spaces. We also study the essential norm of these operators on Fock spaces.