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A Note on the Men'shov-Rademacher Inequality

Witold Bednorz (2006)

Bulletin of the Polish Academy of Sciences. Mathematics

We improve the constants in the Men’shov-Rademacher inequality by showing that for n ≥ 64, E ( s u p 1 k n | i = 1 k X i | ² 0 . 11 ( 6 . 20 + l o g n ) ² for all orthogonal random variables X₁,..., Xₙ such that k = 1 n E | X k | ² = 1 .

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