Sharp Pointwise Estimates for Fock Spaces

Abstract

Let $1\le p<\infty$, and $\alpha >0$. Let $F_{\alpha }^{p}$ denote the Fock space. We establish some sharp pointwise estimates for the derivatives of the functions belonging to $F_{\alpha }^{p}$. Moreover for the Hilbert case $p=2$ we establish some more specific pointwise sharp estimates. We also consider the differential operator between $F_{\alpha }^{p}$ and $F_{\beta }^{p}$ for $\beta >\alpha$ and its adjoint.