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arXiv · 1807.03394

Integral, differential and multiplication operators on generalized Fock spaces

Tesfa Mengestie·Sei-Ichiro Ueki
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Abstract

Volterra companion integral and multiplication operators with holomorphic symbols are studied for a large class of generalized Fock spaces on the complex plane $\CC$. The weights defining these spaces are radial and subject to a mild smoothness condition. In addition, we assumed that the weights decay faster than the classical Gaussian weight. One of our main results show that there exists no nontrivial holomorphic symbols $g$ which induce bounded Volterra companion integral $I_g$ and multiplication operators $M_g$ acting between the weighted spaces. We also describe the bounded and compact Volterra-type integral operators $V_g$ acting between $\mathcal{F}_q^\psi$ and $\mathcal{F}_p^\psi$ when at least one of the exponents $p$ or $q$ is infinite, and extend results of Constantin and Pel\'{a}ez for finite exponent cases. Furthermore, we showed that the differential operator $D$ acts in unbounded fashion on these and the classical Fock spaces.

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Tesfa Mengestie, Sei-Ichiro Ueki. 2018-07-09. Integral, differential and multiplication operators on generalized Fock spaces. https://arxiv.org/abs/1807.03394

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