Weighted LP Boundedness of Pseudodifferential Operators and Applications

被引：11
|
作者：
Michalowski, Nicholas [1 ,2 ]
Rule, David J. [3 ,4 ]
Staubach, Wolfgang [3 ,4 ]
机构：
[1] Univ Edinburgh, Sch Math, Edinburgh EH9 3JZ, Midlothian, Scotland
[2] Univ Edinburgh, Maxwell Inst Math Sci, Edinburgh EH9 3JZ, Midlothian, Scotland
[3] Heriot Watt Univ, Dept Math, Edinburgh EH14 4AS, Midlothian, Scotland
[4] Heriot Watt Univ, Maxwell Inst Math Sci, Edinburgh EH14 4AS, Midlothian, Scotland
来源：
CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES | 2012年 / 55卷 / 03期
基金：
英国工程与自然科学研究理事会;
关键词：
weighted norm inequality; pseudodifferential operator; commutator estimates; SPACES;
D O I：
10.4153/CMB-2011-122-7
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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 Calderon-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 OPS rho,delta m.
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页码：555 / 570
页数：16
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