- Tytuł:
- Maximal Inequalities for a Best Approximation Operator in Orlicz Spaces
- Autorzy:
-
Favier, Sergio
Zó, Felipe - Powiązania:
- https://bibliotekanauki.pl/articles/745344.pdf
- Data publikacji:
- 2011
- Wydawca:
- Polskie Towarzystwo Matematyczne
- Tematy:
-
Best \(\varphi\)-approximations by constants
extended best approximation operator
maximal inequalities - Opis:
- 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.
- Źródło:
-
Commentationes Mathematicae; 2011, 51, 1
0373-8299 - Pojawia się w:
- Commentationes Mathematicae
- Dostawca treści:
- Biblioteka Nauki
Artykuł