Sharp pointwics estimate for Fock spaces

TL;DR

This paper derives sharp pointwise estimates for derivatives of functions in Fock spaces, including specific results for the Hilbert case and analysis of differential operators between different Fock spaces.

Contribution

It provides new sharp pointwise estimates for derivatives in Fock spaces and explores differential operators and their adjoints between these spaces.

Findings

Sharp derivative estimates for Fock space functions.

Specialized estimates in the Hilbert space case.

Analysis of differential operators between 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 $1\leq p<\infty.$ 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.