Fock–Sobolev spaces and their Carleson measures

We study a class of holomorphic spaces Fp,m consisting of entire functions f on Cn such that ∂αf is in the Fock space Fp for all multi-indices α with |α|⩽m. We prove a useful Fourier characterization, namely, f∈Fp,m if and only if zαf(z) is in Fp for all α with |α|=m. We obtain duality and interpolation results for these spaces, including the interesting fact that, for 0