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On the Maximal Lévy–Ottaviani Inequality for Sums of Independent and Dependent Random Vectors

Szewczak Z. S.

Bulletin of the Polish Academy of Sciences. Mathematics

2013

Vol. 61, no 2

155--160

We prove that the sums Sk of independent random vectors satisfy [formula].

Maximal Inequalities for a Best Approximation Operator in Orlicz Spaces

Favier S., Zó F.

Commentationes Mathematicae

2011

Vol. 51, [Z] 1

3-21

In this paper we study a maximal operatorMf related with the best ' approximation by constants for a function [..], where we denote by 'φ'for the derivative function of the C1 convex function φ. We get a necessary and sufficient condition which assure strong inequalities of the type {formula] where K is a constant independent of f. Some pointwise and mean convergence results are obtained. In the particular caseφ^(t) = tp+1 we obtain several equivalent conditions on the functions Θ that assures strong inequalities of this type.