TY - JOUR
T1 - Maximal Inequalities for the Best Approximation Operator and Simonenko Indices
JO - Analysis in Theory and Applications
VL - 3
SP - 253
EP - 266
PY - 2017
DA - 2017/08
SN - 33
DO - http://doi.org/10.4208/ata.2017.v33.n3.6
UR - https://global-sci.org/intro/article_detail/ata/10516.html
KW - Simonenko indices, maximal inequalities, best approximation.
AB - <p style="text-align: justify;">In an abstract set up, we get strong type inequalities in $L^{p+1}$ by assuming &nbsp;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 $\Phi$-approximation operatorsin an Orlicz space $L^{\Phi}$.</p>