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The critical Schatten exponent for the Berger-Coburn endpoint problem
Berger and Coburn showed that boundedness of a Toeplitz operator $T_g$ on the Fock space controls the heat transform $g^{(t)}$ for $1/4<t<1$, and conjectured the endpoint $g^{(1/4)}$ characterizes boundedness. Looi recently disproved this by constructing a bounded $T_g$ with unbounded $g^{(1/4)}$. W
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