International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1990 / Article

Open Access

Volume 13 |Article ID 346835 | https://doi.org/10.1155/S0161171290000527

D. Hajela, "Inequalities for Walsh like random variables", International Journal of Mathematics and Mathematical Sciences, vol. 13, Article ID 346835, 4 pages, 1990. https://doi.org/10.1155/S0161171290000527

Inequalities for Walsh like random variables

Received28 Mar 1988

Abstract

Let (Xn)n1 be a sequence of mean zero independent random variables. Let Wk={j=1kXij|1i1<i2<ik}, Yk=jkWj and let [Yk] be the linear span of Yk. Assume δ|Xn|K for some δ>0 and K>0 and let C(p,m)=16(52p2p1)m1plogp(Kδ)m for 1<p<. We show that for f[Ym] the following inequalities hold:f2fpC(p,m)f2      for2<p<f2C(q,m)fpC(q,m)f2for1<p<2,1p+1q=1and f2C(4,m)2f1C(4,m)2f2. These generalize various well known inequalities on Walsh functions.

Copyright © 1990 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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