L-p-Boundedness for Time-Frequeny Paraproducts, II

Authors

John E. Gilbert
Andrea Nahmod, University of Massachusetts - AmherstFollow

Publication Date

2002

Journal or Book Title

Journal of Fourier Analysis and Applications

Abstract

This article completes the proof of theLp-boundedness of bilinear operators associated to nonsmooth symbols or multipliers begun in Part I, our companion article [8], by establishing the corresponding Lp-boundedness of time-frequency paraproducts associated with tiles in phase plane. The affine invariant structure of such operators in conjunction with the geometric properties of the associated phase-plane decompositions allow Littlewood–Paley techniques to be applied locally, i. e., on trees. Boundedness of the full time-frequency paraproduct then follows using ‘almost orthogonality’ type arguments relying on estimates for tree-counting functions together with decay estimates.

Comments

Publisher's version:

http://link.springer.com/article/10.1007/s00041-002-0006-5

Pages

109-172

Volume

8

Issue

2

Recommended Citation

Gilbert, John E. and Nahmod, Andrea, "L-p-Boundedness for Time-Frequeny Paraproducts, II" (2002). Journal of Fourier Analysis and Applications. 744.
Retrieved from https://scholarworks.umass.edu/math_faculty_pubs/744