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Maximal Inequalities for a Best Approximation Operator in Orlicz Spaces

Sergio FavierFelipe — 2011

Commentationes Mathematicae

In this paper we study a maximal operator f related with the best ϕ approximation by constants for a function f L loc ϕ ' ( n ) , where we denote by ϕ ' derivative function of the C 1 convex function ϕ . We get a necessary and sufficient condition which assure strong inequalities of the type n θ ( | f | ) d x K n θ ( | f | ) d x , where K is a constant independent of f . Some pointwise and mean convergence results are obtained. In the particular case ϕ ( t ) = t p + 1 we obtain several equivalent conditions on the functions θ that assures strong inequalities of this type....

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