On the Hormander Classes of Bilinear Pseudodifferential Operators II

被引：47

作者：

Benyi, Arpad ^{[1
]}

Bernicot, Frederic ^{[2
]}

Maldonado, Diego ^{[3
]}

Naibo, Virginia ^{[3
]}

Torres, Rodolfo H. ^{[4
]}

机构：

[1] Western Washington Univ, Dept Math, Bellingham, WA 98225 USA

[2] Univ Nantes, CNRS, Lab Jean Leray, F-44322 Nantes 3, France

[3] Kansas State Univ, Dept Math, Manhattan, KS 66506 USA

[4] Univ Kansas, Dept Math, Lawrence, KS 66045 USA

来源：

INDIANA UNIVERSITY MATHEMATICS JOURNAL | 2013年 / 62卷 / 06期

基金：

美国国家科学基金会;

关键词：

Bilinear pseudodifferential operators; bilinear Hormander classes; symbolic calculus; Calderon-Zygmund theory; INEQUALITIES; BOUNDEDNESS; LP;

D O I：

10.1512/iumj.2013.62.5168

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Boundedness properties for pseudodifferential operators with symbols in the bilinear Hormander classes of sufficiently negative order are proved. The results are obtained in the scale of Lebesgue spaces, and in some cases, end-point estimates involving weak-type spaces and BMO are provided as well. From the Lebesgue space estimates, Sobolev ones are then easily obtained using functional calculus and interpolation. In addition, it is shown that, in contrast with the linear case, operators associated with symbols of order zero may fail to be bounded on products of Lebesgue spaces.

引用

页码：1733 / 1764

页数：32

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