Sharp pointwics estimate for Fock spaces

Abstract

Firstly we establish a sharp pointwise estimate for the arbitrary derivative of the function $f\in F_{\alpha }^p,$ where $F_{\alpha }^p$ denotes the Fock space for $1\le p<\infty .$ Then, in a particular Hilbert case when $p=2$ we establish another specific pointwise sharp estimate. We also consider the differential operator between $F_{\alpha }^p$ and $F_{\beta }^p$ for $\beta >\alpha$ and its adjoint.

15 pages