A Note on the Men'shov–Rademacher Inequality

Volume 54 / 2006

Witold Bednorz Bulletin Polish Acad. Sci. Math. 54 (2006), 89-93 MSC: Primary 26D15; Secondary 60E15. DOI: 10.4064/ba54-1-9


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 $\sum^n_{k=1}\textbf{E}|X_k|^2=1$.


  • Witold BednorzInstitute of Mathematics
    Warsaw University
    Banacha 2
    02-097 Warszawa, Poland

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