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Fock Projections between Gaussian Mixed-Norm Spaces: Full-Range Boundedness and Compactness
The Fock--Bargmann projection \(P_t\) is initially an orthogonal projection on a Gaussian Hilbert space. We characterize the boundedness and compactness of \[ P_t:L_α^{p_1,q_1}\longrightarrow \mathcal F_β^{p_2,q_2} \] and of its associated maximal projection \[ P_t^+:L_α^{p_1,q_1}\longrightarrow L_β
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