Boundedness of Hardy-Littlewood maximal operator in the framework of Lizorkin-Triebel spaces.

Korry, Soulaymane. "Boundedness of Hardy-Littlewood maximal operator in the framework of Lizorkin-Triebel spaces.." Revista Matemática Complutense 15.2 (2002): 401-416. <http://eudml.org/doc/44373>.

@article{Korry2002,
abstract = {We describe a class O of nonlinear operators which are bounded on the Lizorkin-Triebel spaces Fsp,q(Rn), for 0 &lt; s &lt; 1 and 1 &lt; p, q &lt; ∞. As a corollary, we prove that the Hardy-Littlewood maximal operator is bounded on Fsp,q(Rn), for 0 &lt; s &lt; 1 and 1 &lt; p, q &lt; ∞ ; this extends the result of Kinnunen (1997), valid for the Sobolev space H1p(Rn).},
author = {Korry, Soulaymane},
journal = {Revista Matemática Complutense},
keywords = {Análisis de Fourier; Operador no lineal; Operador maximal de Hardy-Littlewood; Operadores acotados; maximal operator; Hardy-Littlewood maximal operator; Triebel-Lizorkin spaces; boundedness},
language = {eng},
number = {2},
pages = {401-416},
title = {Boundedness of Hardy-Littlewood maximal operator in the framework of Lizorkin-Triebel spaces.},
url = {http://eudml.org/doc/44373},
volume = {15},
year = {2002},
}

TY - JOUR
AU - Korry, Soulaymane
TI - Boundedness of Hardy-Littlewood maximal operator in the framework of Lizorkin-Triebel spaces.
JO - Revista Matemática Complutense
PY - 2002
VL - 15
IS - 2
SP - 401
EP - 416
AB - We describe a class O of nonlinear operators which are bounded on the Lizorkin-Triebel spaces Fsp,q(Rn), for 0 &lt; s &lt; 1 and 1 &lt; p, q &lt; ∞. As a corollary, we prove that the Hardy-Littlewood maximal operator is bounded on Fsp,q(Rn), for 0 &lt; s &lt; 1 and 1 &lt; p, q &lt; ∞ ; this extends the result of Kinnunen (1997), valid for the Sobolev space H1p(Rn).
LA - eng
KW - Análisis de Fourier; Operador no lineal; Operador maximal de Hardy-Littlewood; Operadores acotados; maximal operator; Hardy-Littlewood maximal operator; Triebel-Lizorkin spaces; boundedness
UR - http://eudml.org/doc/44373
ER -