Symbolic calculus and the transposes of bilinear pseudodifferential operators

被引:75
作者
Bényi, A [1 ]
Torres, RH [1 ]
机构
[1] Univ Kansas, Dept Math, Lawrence, KS 66045 USA
基金
美国国家科学基金会;
关键词
bilinear pseudodifferential operators; compound symbols; asymptotic expansion; formal transposes; elementary symbols;
D O I
10.1081/PDE-120021190
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
A symbolic calculus for the transposes of a class of bilinear pseudodifferential operators is developed. The calculus is used to obtain boundedness results on products of Lebesgue spaces. A larger class of pseudodifferential operators that does not admit a calculus is also considered. Such a class is the bilinear analog of the so-called exotic class of linear pseudodifferential operators and fail to produce bounded operators on products of Lebesgue spaces. Nevertheless, the operators are shown to be bounded on products of Sobolev spaces with positive smoothness, generalizing the Leibniz rule estimates for products of functions.
引用
收藏
页码:1161 / 1181
页数:21
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