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Maximal Inequalities for a Best Approximation Operator in Orlicz Spaces

100%

Favier S., Zó F.

Commentationes Mathematicae

2011

tom 51

nr 1

In this paper we study a maximal operator \(\mathcal{M}f\) related with the best \(\varphi\) approximation by constants for a function \(f\in L^{\varphi'}_{\text{loc}}(\mathbb{R}^n)\), where we denote by \(\varphi'\) derivative function of the \(C^1\) convex function \(\varphi\). We get a necessary and sufficient condition which assure strong inequalities of the type \(\int_{\mathbb{R}^n} \theta(\mathcal{M}|f|)dx\leq K \int_{\mathbb{R}^n} \theta(|f|) dx\), where \(K\) is a constant independent of \(f\). Some pointwise and mean convergence results are obtained. In the particular case \(\varphi (t) = t^{p+1}\) we obtain several equivalent conditions on the functions \(\theta\) that assures strong inequalities of this type.

On functions satisfying a local Lipschitz condition of order α

40%

Zó F.

Studia Mathematica

1980

tom 68

nr 2

107-116

Ograniczanie wyników

1 Commentationes Mathematicae

1 Studia Mathematica

2 Zó F.

1 Favier S.

1 2011

1 1980

Wyniki wyszukiwania

Maximal Inequalities for a Best Approximation Operator in Orlicz Spaces

On functions satisfying a local Lipschitz condition of order α