An independent proof establishes the sharp log-free L^2 to L^{10/3} endpoint estimate for the two-dimensional Hermite operator.
Escauriaza,Carleman inequalities and the heat operator, Duke Math
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Sharp Endpoint Eigenfunction Estimates for the Two-Dimensional Hermite Operator
An independent proof establishes the sharp log-free L^2 to L^{10/3} endpoint estimate for the two-dimensional Hermite operator.