Sharp Gaussian Mixed-Norm Theory for Fock Spaces

We develop a structural theory of the Gaussian mixed-norm Fock spaces $\mathcal F_α^{p,q}$, where $α>0$ and $0<p,q\leq\infty$, which separate angular $L^p$-means from radial Gaussian $L^q$-summability. We first prove the sharp circle-mean estimate $M_p(f,r)\leq C_{α,q}(1+r)^{-\frac{1}{q}} e^{\fracα{