The existence of an extremal in an exponential Sobolev type inequality, with optimal constant, in Gauss space is established. A key step in the proof is an augmented version of the relevant inequality, which, by contrast, fails for a parallel classical inequality by Moser in the Euclidean space.

中文翻译：

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关于高斯空间中Moser型不等式极值的存在性

建立了在高斯空间中具有最优常数的指数 Sobolev 型不等式中极值的存在性。证明中的一个关键步骤是相关不等式的增强版本，相比之下，Moser 在欧几里得空间中的平行经典不等式失败。