Product of Volterra-Type Integral and Composition Operators on Quaternionic Fock Spaces

Abstract

We characterize products of Volterra-type integral operators and composition operators acting between quaternionic Fock spaces for the full range \(0<p,q<\infty\), allowing general slice regular composition symbols without any slice-preserving assumption. The criteria are formulated in terms of a Berezin-type testing quantity. Using a fixed-slice matrix realization of the \(\star\)-product, we express slice composition through a matrix functional calculus and relate the testing quantity to complex Berezin-type estimates associated with the eigenvalue maps of the matrix symbol. We also show that the natural affine restrictions are imposed on these eigenvalue functions rather than on the composition symbol itself.