ESSENTIAL NORMS OF INTEGRAL OPERATORS

. We estimate the essential norms of Volterra-type integral operators V g and I g , and multiplication operators M g with holomorphic symbols g on a large class of generalized Fock spaces on the complex plane C . The weights defining these spaces are radial and subjected to a mild smoothness conditions. In addition, we assume that the weights de- cay faster than the classical Gaussian weight. Our main result estimates the essential norms of V g in terms of an asymptotic upper bound of a quantity involving the inducing symbol g and the weight function, while the essential norms of M g and I g are shown to be comparable to their operator norms. As a means to prove our main results, we first charac-terized the compact composition operators acting on the spaces which is interest of its own.

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