Fock Projections on Mixed Norm Spaces

In this paper, we completely characterize \(L^{p,q}\) $L^{p,q}$ -boundedness of (maximal) Fock projections on \(\mathbb {C}\) $\mathbb{C}$ for \(1\le p,q\le \infty \) $1\le p,q\le \infty$ . As applications, we identify the dual space of mixed norm space \(F_\alpha ^{p,q}\) $F_{\alpha }^{p,q}$ of entire functions and present an alternative proof of the Littlewood–Paley formula for \(F_\alpha ^{p,q}\) $F_{\alpha }^{p,q}$ .