Abstract
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<p⩽1, (Fp,m)⁎=F∞,m. We also characterize Carleson measures for Fp,m in terms of simple polynomial growth conditions.
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