Geodesic
Weighted Lp Boundedness of Pseudodifferential Operators and Applications
Canadian mathematical bulletin, Tome 55 (2012) no. 3, pp. 555-570

Voir la notice de l'article provenant de la source Cambridge

DOI

In this paper we prove weighted norm inequalities with weights in the ${{A}_{p}}$ classes, for pseudodifferential operators with symbols in the class $S_{\rho ,\delta }^{n(\rho -1)}$ that fall outside the scope of Calderón–Zygmund theory. This is accomplished by controlling the sharp function of the pseudodifferential operator by Hardy–Littlewood type maximal functions. Our weighted norm inequalities also yield ${{L}^{p}}$ boundedness of commutators of functions of bounded mean oscillation with a wide class of operators in $\text{OPS}_{\rho ,\delta }^{m}$ .
DOI : 10.4153/CMB-2011-122-7
Mots-clés : 42B20, 42B25, 35S05, 47G30, weighted norm inequality, pseudodifferential operator, commutator estimates 
Michalowski, Nicholas; Rule, David J.; Staubach, Wolfgang. Weighted Lp Boundedness of Pseudodifferential Operators and Applications. Canadian mathematical bulletin, Tome 55 (2012) no. 3, pp. 555-570. doi: 10.4153/CMB-2011-122-7
@article{10_4153_CMB_2011_122_7,
     author = {Michalowski, Nicholas and Rule, David J. and Staubach, Wolfgang},
     title = {Weighted {Lp} {Boundedness} of {Pseudodifferential} {Operators} and {Applications}},
     journal = {Canadian mathematical bulletin},
     pages = {555--570},
     year = {2012},
     volume = {55},
     number = {3},
     doi = {10.4153/CMB-2011-122-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-122-7/}
}
TY  - JOUR
AU  - Michalowski, Nicholas
AU  - Rule, David J.
AU  - Staubach, Wolfgang
TI  - Weighted Lp Boundedness of Pseudodifferential Operators and Applications
JO  - Canadian mathematical bulletin
PY  - 2012
SP  - 555
EP  - 570
VL  - 55
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-122-7/
DO  - 10.4153/CMB-2011-122-7
ID  - 10_4153_CMB_2011_122_7
ER  - 
%0 Journal Article
%A Michalowski, Nicholas
%A Rule, David J.
%A Staubach, Wolfgang
%T Weighted Lp Boundedness of Pseudodifferential Operators and Applications
%J Canadian mathematical bulletin
%D 2012
%P 555-570
%V 55
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-122-7/
%R 10.4153/CMB-2011-122-7
%F 10_4153_CMB_2011_122_7

Cité par Sources :