Domination inequality for martingale transforms of a Rademacher sequence

@article{Hitczenko1993DominationIF,
  title={Domination inequality for martingale transforms of a Rademacher sequence},
  author={Pawel Hitczenko},
  journal={Israel Journal of Mathematics},
  year={1993},
  volume={84},
  pages={161-178}
}
AbstractLetfn = Σk=1nvkrk,n=1,…, be a martingale transform of a Rademacher sequence (rn)and let (rn′) be an independent copy of (rn).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… CONTINUE READING