Essential norms of integral operators
J. Korean Math. Soc. 2019 Vol. 56, No. 2, 523-537
Published online 2019 Mar 01
Tesfa Mengestie
Western Norway University of Applied Sciences
Abstract : 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 $\mathbb {C}$. The weights defining these spaces are radial and subjected to a mild smoothness conditions. In addition, we assume that the weights decay 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 characterized the compact composition operators acting on the spaces which is interest of its own.
Keywords : generalized Fock spaces, Volterra-type integral operator, multiplication operator, essential norm, composition operator
MSC numbers : Primary 30H20, 47B32; Secondary 46E22, 46E20, 47B33
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