Maximal Inequalities for a Best Approximation Operator in Orlicz Spaces

• Autorzy: Sergio Favier , Felipe Zó
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Best \(\varphi\)-approximations by constants; extended best approximation operator; maximal inequalities

• Wydawca: Polish Mathematical Society
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2011
• Tom: 51
• Numer: 1

Daty

wydano

2011

online

2017-12-19

Twórcy

autor

Sergio Favier

autor

Felipe Zó

Identyfikatory

DOI

10.14708/cm.v51i1.5305