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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.
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참고문헌 (22)
참고문헌 신청
A. Aleman / 2007 / Topics in complex analysis and operator theory / Univ. Malaga :3~30
B. J. Carswell / 2003 / Composition operators on the Fock space / Acta Sci. Math. (Szeged) 69(3-4):871~887
S. Chandrasekhar / 1950 / Radiative Transfer / Oxford University Press
O. Constantin / 2012 / A Volterra-type integration operator on Fock spaces / Proc. Amer. Math. Soc 140(12):4247~4257
O. Constantin / 2016 / Integral operators, embedding theorems and a Littlewood-Paley formula on weighted Fock spaces / J. Geom. Anal 26(2):1109~1154
B. J. Carswell / 2003 / Composition operators on the Fock space / Acta Sci. Math. (Szeged) 69(3-4):871~887
S. Chandrasekhar / 1950 / Radiative Transfer / Oxford University Press
O. Constantin / 2012 / A Volterra-type integration operator on Fock spaces / Proc. Amer. Math. Soc 140(12):4247~4257
O. Constantin / 2016 / Integral operators, embedding theorems and a Littlewood-Paley formula on weighted Fock spaces / J. Geom. Anal 26(2):1109~1154
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