On the best constants in the Khinchin inequality

By S. Szarek. 1976

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Inference Under Information Constraints I: Lower Bounds From Chi-Square Contraction (2018, background): “For Z = V Y described above, we have Therefore, by Khintchine’s inequality ( cf. [46]), where v 1 , . . . , v k/ 2 denote the row vectors of the matrix V .”
A Vector-Contraction Inequality for Rademacher Complexities (2016, background): “ that for every v∈ ℓ2 kvk ≤ CE X∞ k=1 Xkvk . The proof, given below, is easy and modeled after the proof of the Khintchine inequalities in [10]. For Rademacher variables the best constant is C = √ 2 ([19], see also inequality (4.3) in [10] or Theorem 5.20 in [?]). In the standard normal case the ine”
Prediction, learning, and games (2006, background): “The form of Khinchine’s inequality cited here is due to Szarek [281].”
Graphons, cut norm and distance, couplings and rearrangements (2010, background): “Furthermore, the constant √ 3, which is implicit in [46], has been improved to √ 2 by Szarek [57].”
Inequalities and limit theorems for weakly dependent sequences (2013, background): “Now, by the lower bound of Szarek (1976) in Khinchin’s inequality, for any finite sequence a1, .”
Analysis in Banach Spaces (2023, background): “2 Excellent introductions to the theory of C0-semigroups include the monographs Davies [1980], Engel and Nagel [2000], Goldstein [1985], Pazy [1983], Tanabe [1979]. The monumental 1957 treatise of Hille and Phillips [1957] is freely available on-line (http://www.”
Uniform Hanson-Wright type concentration inequalities for unbounded entries via the entropy method (2018, background): “Then, E‖Bε‖2 = ‖B‖2HS and by Khinchin’s inequality it holds E‖Bε‖ ≥ 1√ 2 ‖B‖HS , with the optimal constant due to Szarek (1976).”