ISRAEL JOURNAL OF MATHEMATICS S4 (1993)~ 161-178 DOMINATION INEQUALITY FOR MARTINGALE TRANSFORMS OF A RADEMACHER SEQUENCE BY PAWEL HITCZENKO* Department of Mathematics North Carolina State University, Raleigh, NU s USA ABSTRACT Let .f,~ ---- ~"]~=lv~r~, n ---- 1,..., be a martingale transform of a Rademacher sequence (r,) and let (r~) be an independent copy of (rn). The main result of this paper states that there exists an absolute constant K such that for all p, 1 _<p < oo, the following inequality is true: 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,~) one has ] Eahrk P ~-~l,,((aa),~/P'-), where KI,2 ((a.), V~) ----K((a.), ~; 11,12) is the K-interpolation norm between Ii and l]. We also derive a new exponential inequality for mar- tingale transforms of a Rademacher sequence. 1. Introduction This paper concerns the Lp-norm inequalities for certain martingale transforms. Let (f/, jr, p) be a probability space. Let (~'n) be an increasing sequence of sub-a- algebras of~-. A sequence (Xn) of random variables is said to be (Y-'n)-predictable (or just predictable, if there is no risk of confusion) provided for each n > 1, Xn is * This research was supported in part by an NSF grant and an FRPD grant at NCSU. Received August 24, 1992 and in revisedform January 12, 1993 161