Document Type

Article

Publication Date

2013

Keywords

Bilinear pseudodifferential operators, Bilinear Hormander classes, Symbolic calculus, Calderon-Zygmund theory

Abstract

Boundedness properties for pseudodifferential operators with symbols in the bilinear Hörmander 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.

Publication Title

Indiana University Mathematics Journal

Volume

62

Issue

6

First Page

1733

Last Page

1764

Required Publisher's Statement

Published by the Indiana University Mathematics Journal, 2013

DOI: 10.1512/iumj.2013.62.5168

Link to publisher version of article: http://www.iumj.indiana.edu/IUMJ/FULLTEXT/2013/62/5168

Language

English

Format

application/pdf

Included in

Mathematics Commons

Share

COinS