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
DOI
http://dx.doi.org/10.1512/iumj.2013.62.5168
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
Recommended Citation
Arpad Benyi, Frederic Bernicot, Diego Maldonado, Virginia Naibo, Rodolfo H.Torres, On the Hormander classes of bilinear pseudodifferential operators II, Indiana Univ. Math. J. 62 (2013), 1733-1764
Subjects - Topical (LCSH)
Pseudodifferential operators; Decomposition method; Calderón-Zygmund operator; Bilinear transformation method; Calculus
Genre/Form
articles
Type
Text
Rights
Copying of this document in whole or in part is allowable only for scholarly purposes. It is understood, however, that any copying or publication of this document for commercial purposes, or for financial gain, shall not be allowed without the author’s written permission.
Language
English
Format
application/pdf
