Fourier transform and Radon transform for mixed Hodge modules

We give a generalization to bi-filtered D-modules underlying mixed Hodge modules of the relation between microlocalization along f 1 , ⋯ , f r ∈ 𝒪 X ( X ) and vanishing cycles along g = ∑ i = 1 r y i f i . This leads to an interesting relation between localization triangles. As an application, we use these results to compare the k -plane Radon transform and the Fourier–Laplace transform for mixed Hodge modules. This is then applied to the Hodge module structure of certain GKZ systems.