Geodesic
A Note on the Men'shov–Rademacher Inequality
Witold Bednorz1
1 Institute of Mathematics Warsaw University Banacha 2 02-097 Warszawa, Poland
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 54 (2006) no. 1, pp. 89-93.

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We improve the constants in the Men'shov–Rademacher inequality by showing that for $n\ge 64$, $$ \textbf{E}\Big(\sup_{1\le k\le n}\Big|\sum^k_{i=1} X_i\Big|^2\Big)\le 0.11(6.20+\log_2 n)^2 $$ for all orthogonal random variables $X_1,\ldots ,X_n$ such that $\sum^n_{k=1}\textbf{E}|X_k|^2=1$.
DOI : 10.4064/ba54-1-9
Keywords: improve constants menshov rademacher inequality showing textbf sup sum log orthogonal random variables ldots sum textbf

Witold Bednorz 1

1 Institute of Mathematics Warsaw University Banacha 2 02-097 Warszawa, Poland 
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Witold Bednorz. A Note on the Men'shov–Rademacher Inequality. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 54 (2006) no. 1, pp. 89-93. doi : 10.4064/ba54-1-9. http://geodesic.mathdoc.fr/articles/10.4064/ba54-1-9/

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