Year: 2026
Type: preprint
Abstract: Berger and Coburn showed that boundedness of a Toeplitz operator $T_g$ on the Fock space controls the heat transform $g^{(t)}$ for $1/41$. Our counterexamples come from Baire category and closed graph arguments, which yield no explicit symbols. Despite this two-sided failure, the forward implication has a sharp Schatten-class form: $\|g^{(1/4)}\|_\infty\le 2^n\|T_g\|_{S_1}$ for every admissible symbol $g$ with $T_g$ trace class. We show that the constant $2^n$ is optimal and that the same estimate holds with $S_p$ in place of $S_1$ for $T_g\in S_p$ when $01$, no corresponding uniform estimate holds, even for smooth compactly supported symbols. We also determine the optimal constants in the Berger--Coburn estimates for $1/4
Source: arXiv (Cornell University)
Author: Virtanen, Jani A.
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212222549