Publication Date
2001
Journal or Book Title
Journal of Fourier Analysis and Applications
Abstract
This paper proves the Lp-boundedness of general bilinear operators associated to a symbol or multiplier which need not be smooth. The Main Theorem establishes a general result for multipliers that are allowed to have singularities along the edges of a cone as well as possibly at its vertex. It thus unifies ealier results of Coifman-Meyer for smooth multipliers and ones, such the Bilinear Hilbert transform of Lacey-Thiele, where the multiplier is not smooth. Using a Whitney decomposition in the Fourier plane a general bilinear operator is represented as infinite discrete sums of time-frequency paraproducts obtained by associating wave-packets with tiles in phase-plane. Boundedness for the general bilinear operator then follows once the corresponding Lp-boundedness of time-frequency paraproducts has been established. The latter result is the main theorem proved in Part II, our subsequent paper [11], using phase-plane analysis.
Pages
435-467
Volume
7
Issue
5
Recommended Citation
Gilbert, John E. and Nahmod, Andrea R., "Bilinear Operators with Non-Smooth Symbol, I" (2001). Journal of Fourier Analysis and Applications. 745.
Retrieved from https://scholarworks.umass.edu/math_faculty_pubs/745
Comments
This is the author's version. Publisher's version:
http://link.springer.com/article/10.1007/BF02511220