Uniform almost sub-Gaussian estimates for linear functionals on convex sets

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A Berry-Esseen type inequality for convex bodies with an unconditional basis (2007, methodology): “istic function of the cube [− √ 3, √ 3]n. Proof of Lemma 7.2: The case n= 1 is covered, e.g., in [28]. We assume from now on that n≥ 2. Our method builds on the main idea of the proof of Lemma 2.3 in [23]. Fix x∈ Rn. We claim that |∇f(x)| ≤ C1nf(x)−C2∇f(x)·x, (42) for some universal constants C1,C2 ”
Centroid Bodies and the Logarithmic Laplace Transform - A Unified Approach (2011, background): “(Zp(μ)) involving the “tilts” of the measure μ from [15, 16], and we relate between the Zp-bodies of the original measure and its tilts.”