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arXiv · 2609.11853

The critical Schatten exponent for the Berger-Coburn endpoint problem

Jani A. Virtanen
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Abstract

Berger and Coburn showed that boundedness of a Toeplitz operator $T_g$ on the Fock space controls the heat transform $g^{(t)}$ for $1/4 1$, no corresponding $S_p$ estimate is possible, even for compactly supported smooth symbols. Moreover, a Baire category argument shows there is an admissible symbol $g$ with $T_g\in S_p$ for every $p>1$ while $g^{(1/4)}$ is unbounded, though it yields no explicit symbol. We also determine the optimal constants in the Berger--Coburn estimates for $1/4<t\leq1$.

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Jani A. Virtanen. 2026-09-10. The critical Schatten exponent for the Berger-Coburn endpoint problem. https://arxiv.org/abs/2609.11853

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