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The strongp-variation of martingales and orthogonal series

Authors:

Affiliation:

1. Texas A & M University, 77843, College Station, TX
2. Equipe D'analyse, Wuhan University and Université Paris VI, Tour 46, 4ème Etage, 4, Place Jussieu, F-75252, Paris Cedex 05, France

Abstract:

Let 1

and letx=(x_n)n0 be a sequence of scalars. The strongp-variation ofx, denoted byW_p(x), is defined as

$W_p (x) = sup left{ {left( {\|x_0 \|^p + sumlimits_{k = 1}^infty {\|x_{n_k } - x_{n_{k - 1} } \|^p } } right)^{1/p} } right}$

Keywords:
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