Domination inequality for martingale transforms of a Rademacher sequence期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

Domination inequality for martingale transforms of a Rademacher sequence

Authors:	Pawe? Hitczenko

Institution:	(1) Department of Mathematics, North Carolina State University, 27695-8205 Raleigh, NC, USA

Abstract:	Letf _n = Σ _k=1 ⁿ v _k r _k,n=1,…, be a martingale transform of a Rademacher sequence (r _n)and let (r _n ^′ ) be an independent copy of (r _n).The main result of this paper states that there exists an absolute constantK such that for allp, 1≤p<∞, the following inequality is true: $\left\\| {\sum {v_k r_k } } \right\\|_p \leqslant K\left\\| {\sum {v_k r_k^\prime } } \right\\|_p$ In order to prove this result, we obtain some inequalities which may be of independent interest. In particular, we show that for every sequence of scalars (a _n)one has $\left\\| {\sum {v_k r_k } } \right\\|_p \approx K_{1,2} ((a_n )),\sqrt p$ where $K_{1,2} ((a_n ),\sqrt p ) = K_{1,2} ((a_n ),\sqrt p ;\ell _1 ,\ell _2 )$ is theK-interpolation norm between ℓ₁ and ℓ₂. We also derive a new exponential inequality for martingale transforms of a Rademacher sequence. This research was supported in part by an NSF grant and an FRPD grant at NCSU.

Keywords:
本文献已被 SpringerLink 等数据库收录！