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Sharp Gaussian divergence and Bernstein-Markov inequalities
We prove two dimension-free estimates in Gaussian space. The first is an optimal Meyer-type inequality for the Gaussian divergence: for $p\geq2$, \[ \|δV\|_{L^p(γ_d)} \leq \sqrt p\,|\mathbb E V| +Cp\,\|DV\|_{L^p(γ_d;\mathrm{HS}_d)}\, . \] Here $\mathrm{HS}_d$ is the space of $d\times d$ matric
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