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Volume 33, Issue 3
Maximal Inequalities for the Best Approximation Operator and Simonenko Indices

S. Acinas & S. Favier

DOI: 10.4208/ata.2017.v33.n3.6

Anal. Theory Appl., 33 (2017), pp. 253-266.

Published online: 2017-08

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  • Abstract

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 $\Phi$-approximation operatorsin an Orlicz space $L^{\Phi}$.

  • Keywords

Simonenko indices, maximal inequalities, best approximation.

  • AMS Subject Headings

41A10, 41A50, 41A45

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{ATA-33-253, author = {S. Acinas and S. Favier}, title = {Maximal Inequalities for the Best Approximation Operator and Simonenko Indices}, journal = {Analysis in Theory and Applications}, year = {2017}, volume = {33}, number = {3}, pages = {253--266}, abstract = {

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 $\Phi$-approximation operatorsin an Orlicz space $L^{\Phi}$.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2017.v33.n3.6}, url = {http://global-sci.org/intro/article_detail/ata/10516.html} }
TY - JOUR T1 - Maximal Inequalities for the Best Approximation Operator and Simonenko Indices AU - S. Acinas & S. Favier 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 -

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 $\Phi$-approximation operatorsin an Orlicz space $L^{\Phi}$.

S. Acinas and S. Favier. (2017). Maximal Inequalities for the Best Approximation Operator and Simonenko Indices. Analysis in Theory and Applications. 33 (3). 253-266. doi:10.4208/ata.2017.v33.n3.6
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