Document Type

Article

Publication Date

2010

Keywords

Bilinear pseudodifferential operators, Bilinear Hörmander classes, Symbolic calculus, Calderón–Zygmund theory

Abstract

Bilinear pseudodifferential operators with symbols in the bilinear analog of all the Hörmander classes are considered and the possibility of a symbolic calculus for the transposes of the operators in such classes is investigated. Precise results about which classes are closed under transposition and can be characterized in terms of asymptotic expansions are presented. This work extends the results for more limited classes studied before in the literature and, hence, allows the use of the symbolic calculus (when it exists) as an alternative way to recover the boundedness on products of Lebesgue spaces for the classes that yield operators with bilinear Calderón–Zygmund kernels. Some boundedness properties for other classes with estimates in the form of Leibniz’ rule are presented as well.

Publication Title

Integral Equations and Operator Theory

Volume

67

Issue

3

First Page

341

Last Page

364

DOI

http://dx.doi.org/ 10.1007/s00020-010-1782-y

Required Publisher's Statement

© Springer International Publishing AG

The final publication is available at Springer via http://dx.doi.org/ 10.1007/s00020-010-1782-y

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

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Mathematics Commons

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