PARAPRODUCTS
Time-frequency analysis of paraproducts
| Coordinatore | UNIVERSITY OF GLASGOW
Organization address
address: University Avenue contact info |
| Nazionalità Coordinatore | United Kingdom [UK] |
| Totale costo | 161˙792 € |
| EC contributo | 161˙792 € |
| Programma | FP7-PEOPLE
Specific programme "People" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) |
| Code Call | FP7-PEOPLE-2007-2-1-IEF |
| Funding Scheme | MC-IEF |
| Anno di inizio | 2008 |
| Periodo (anno-mese-giorno) | 2008-10-15 - 2010-10-14 |
Partecipanti
| # | ||||
|---|---|---|---|---|
| 1 |
UNIVERSITY OF GLASGOW
Organization address
address: University Avenue contact info |
UK (GLASGOW) | coordinator | 0.00 |
Mappa
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Obiettivo del progetto (Objective)
'Singular integral operators form one of the most important classes of operators in Mathematical Analysis and its applications. Paraproducts are special operators from this class, which are at the same time the 'building blocks' for general singular integral operators. These special singular integral operators are particularly useful in the study of certain partial differential equations . Similarly to multiplier operators like the classical Hilbert transform, they are characterized by the fact that their frequency singularity is localized in a single point. In the last ten years, there has been huge interest for a new kind of singular integrals: so-called modulation invariant Calderón-Zygmund operators, which main feature is that their frequency singularities are spread over large varieties. This is for example the case for the bilinear Hilbert transform, whose singularities localize in a line in the plane. Our project proposes the study of tensor products of singular integrals that mix both types of singularities, since these are defined by a symbol given by the product of a classical paraproduct symbol and a modulation invariant one. The main tool for such a task will be the time-frequency analysis, which has already been applied to great success in the modulation invariant setting. This project can be considered as the next basic step in the future evolution of modern singular integral theory.'