We describe a class O of nonlinear operators which are bounded on the Lizorkin-Triebel spaces Fs p,q(Rn), for 0 < s < 1 and 1 < p, q < ∞. As a corollary, we prove that the Hardy-Littlewood maximal operator is bounded on Fs p,q(Rn), for 0 < s < 1 and 1 < p, q < ∞ ; this extends the result of Kinnunen (1997), valid for the Sobolev space H1 p(Rn).
@article{urn:eudml:doc:44373,
title = {Boundedness of Hardy-Littlewood maximal operator in the framework of Lizorkin-Triebel spaces.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {15},
year = {2002},
pages = {401-416},
zbl = {1033.42013},
mrnumber = {MR1951818},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44373}
}
Korry, Soulaymane. Boundedness of Hardy-Littlewood maximal operator in the framework of Lizorkin-Triebel spaces.. Revista Matemática de la Universidad Complutense de Madrid, Tome 15 (2002) pp. 401-416. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44373/