Dr Pierre Portal
Maitre de conférence, Université Lille 1 .Research Interests
I am a mathematical analyst. The questions I am interested in are related to problems in a variety of applied fields, ranging from (stochastic and deterministic) partial differential equations to signal processing, but, for me, they are questions about operators acting on Banach spaces. My particular focus is on a type of inequalities called square function estimates. These estimates are fundamentally harmonic analytic estimates; the Litllewood-Paley are the quintessential examples, and Calderón-Zygmund theory as well as wavelet theory rely heavily on them. They are, however, quite ubiquitous, and appear in various guises in operator theory, geometry of Banach spaces, stochastic integration, ergodic theory... Over the last years I have thus been contemplating these estimates in quite distinct problems, but my techniques to prove them or use them kept revolving around probabilistic Littlewood-Paley theory. Recently I have been mostly working on new Hardy spaces (which norms are given by square functions) with the aim of bringing to stochastic PDE analogues of the tools available to deterministic PDE through classical Hardy spaces theory.
ContactUniversite des Sciences et Technologies de LilleLaboratoire Paul Painleve UMR 8524, UFR de Mathematiques 59655 Villeneuve d'Ascq Cedex FRANCE Email : Pierre.Portal AT math.univ-lille1.fr |
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