Sobolev Space Estimates and Symbolic Calculus for Bilinear Pseudodifferential Operators

Authors

Arpad Benyi
Andrea R. Nahmod, University of Massachusetts AmherstFollow
Rodolpho H. Torres

Publication Date

2006

Journal or Book Title

JOURNAL OF GEOMETRIC ANALYSIS

Abstract

Bilinear operators are investigated in the context of Sobolev spaces and various techniques useful in the study of their boundedness properties are developed. In particular, several classes of symbols for bilinear operators beyond the so-called Coifman-Meyer class are considered. Some of the Sobolev space estimates obtained apply to both the bilinear Hilbert transform and its singular multipliers generalizations as well as to operators with variable dependent symbols. A symbolic calculus for the transposes of bilinear pseudodifferential operators and for the composition of linear and bilinear pseudodifferential operators is presented too.

Comments

Publisher's version here:

http://link.springer.com/article/10.1007/BF02922061

Pages

431-453

Volume

16

Issue

3

Recommended Citation

Benyi, Arpad; Nahmod, Andrea R.; and Torres, Rodolpho H., "Sobolev Space Estimates and Symbolic Calculus for Bilinear Pseudodifferential Operators" (2006). JOURNAL OF GEOMETRIC ANALYSIS. 738.
Retrieved from https://scholarworks.umass.edu/math_faculty_pubs/738