Károly J. Böröczky, Yaozhong W. Qiu, Cyril Roberto
We prove an $L^2$-stability estimate for the variance Brascamp-Lieb inequality [J. Funct. Anal. 22 (4), 366-389 (1976)] by bootstrapping the recent $L^1$-stability theorem of Machado and Ramos [arXiv:2511.22636] under an additional assumption, which we call the super-Brascamp-Lieb inequality, of independent interest.
Károly J. Böröczky, Yaozhong W. Qiu, Cyril Roberto
This paper contains 8 sections, 7 theorems, 74 equations.
Theorem 2.1
Let $f: \mathbb{R}^n \rightarrow \mathbb{R}$ be smooth, such that $\varepsilon \coloneq \int \langle (V")^{-1} f', f' \rangle d\mu_V - \mathop{\mathrm{Var}}\nolimits_{\mu_V}(f) > 0$ and $\int fd\mu_V = 0$. Suppose that for any $g: \mathbb{R}^n \rightarrow \mathbb{R}$ smooth for some $\delta \in (0, 1)$ and some $C_0 > 0$. Then there exists $\theta = \theta(f) \in \mathbb{R}^n$ such that with $C
