Maximal Inequalities for the Best Approximation Operator and Simonenko Indices (Analysis in Theory and Applications, 2017)
In an abstract set up, we get strong type inequalities in $L^{p+1}$ by assuming weak or extra-weak inequalities 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 operatorsin an Orlicz space $L^{Φ}$.
Keywords: Simonenko indices; maximal inequalities; best approximation.