Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 2 of 2
Full-Text Articles in Physical Sciences and Mathematics
Bilinear Operators With Non-Smooth Symbol, I, John E. Gilbert, Andrea R. Nahmod
Bilinear Operators With Non-Smooth Symbol, I, John E. Gilbert, Andrea R. Nahmod
Mathematics and Statistics Department Faculty Publication Series
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 …
Boundedness Of Bilinear Operators With Nonsmooth Symbols, John Gilbert, Andrea Nahmod
Boundedness Of Bilinear Operators With Nonsmooth Symbols, John Gilbert, Andrea Nahmod
Mathematics and Statistics Department Faculty Publication Series
We announce the Lp-boundedness of general bilinear operators associated to a symbol or multiplier which need not be smooth. We establish 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 CoifmanMeyer for smooth multipliers and ones, such the Bilinear Hilbert transform of Lacey-Thiele, where the multiplier is not smooth.