Maximal Inequalities for the best polynomial approximation operators and Simonenko indices

Abstract

In an abstract set up, we get strong type inequalities in L^p+1 by assuming weak or extra-weak inequalitie in Orlicz spaces. For some classes of functions, the number p is related to Simonenko indices. We apply the results to get strong inequalities for maximal functions associated to best Φ-approximation operators in an Orlicz space L-Φ.