JIPAM
| On Maximal Inequalities Arising in Best Approximation | ||||
| Authors: | F. D. Mazzone, F. Zó, | |||
| Keywords: | Best approximants, $arPhi$-approximants, $sigma$-lattices, Maximal inequalities. | |||
| Date Received: | 07/11/06 | |||
| Date Accepted: | 02/06/09 | |||
| Subject Codes: |
Pri: 41A30; Sec: 41A65. |
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| Editors: | Sever S. Dragomir, | |||
| Abstract: |
Let | |||
be a function in an Orlicz space 
and 
be the set of all the best 
-approximants to 
given a 
lattice 
Weak type inequalities are proved for the maximal operator 
where 
is any selection of functions in 
and 
is an increasing sequence of 
-lattices. Strong inequalities are proved in an abstract set up which can be used for an operator as 
.;
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