Full paper in PDF:
$%S. Korry, Boundedness of Hardy-Littlewood maximal operator in the framework of Lizorkin-Triebel spaces, Rev. Mat. Complut. 15 (2002), no. 2, 401–416.%$

Boundedness of Hardy-Littlewood Maximal Operator in the Framework of Lizorkin-Triebel Spaces
Soulaymane KORRY
Equipe d’Analyse et de Mathématiques Appliquées
bâtiment Copernic, Université de Marne-La-Vallée
5 Bd Descartes, Champs-sur-Marne
77454 Marne-La-Vallée Cedex 2 — France
korry@math.univ-mlv.fr

Received: July 4, 2001
Revised: March 7, 2002

ABSTRACT

We describe a class O of nonlinear operators which are bounded on the Lizorkin–Triebel spaces Fs (ℝn) p,q , for 0 <s < 1 and 1< p,q < ∞ . As a corollary, we prove that the Hardy-Littlewood maximal operator is bounded on Fsp,q(ℝn ) , for 0< s< 1 and 1< p,q < ∞ ; this extends the result of Kinnunen (1997), valid for the Sobolev space H1p(ℝn ) .

2000 Mathematics Subject Classification: 42B25.