A Volterra-type integration operator on Fock spaces

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We study certain spectral properties and the invariant subspaces for some classes of integration operators of Volterra type on the Fock space.

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Integral Operators, Embedding Theorems and a Littlewood–Paley Formula on Weighted Fock Spaces (2013, background): “The corresponding results for the classical Fock space can be found in [11].”
Integral operators on analytic Morrey spaces (2013, background): “Constantin [9] studied the boundedness and the compactness of Tg on Fock spaces.”
Integration operators between Hardy spaces on the unit ball of $\Cn$ (2013, unknown): “After the pioneering works of Aleman, Siskakis and Cima [4, 6, 7] describing the boundedness and compactness of the operator Jg in Hardy and Bergman spaces, the mentioned operator became extremely popular, being studied in many spaces of analytic functions (see [4, 5, 6, 7, 13, 27, 28] for example).”