Lecturers

Laura Keller, Tristan Rivière

Assistant

Alessandro Pigati

When and where

Thursday, 13:15 - 15:00, HG G 43 (starting from March 2nd)

We will first briefly recall the general Littlewood-Paley theory (LP theory). After this review, we shall study applications of this theory to important problems relevant to the analysis of Partial Differential Equations which constitutes the main topics of the seminar.
Littlewood-Paley characterizations of commonly used spaces in PDE such as Sobolev, Besov, Hardy, BMO spaces... etc. will be first presented. Then some sessions will be devoted to the use of LP theory to interpolation inequalities. Finally, we will introduce the notion of Paraproducts and its application to the analysis of various products and non-linearity in various function spaces.
The first hours of the seminar will be given by the organizers themselves. The participants will then be asked to take over the rest of the seminar by choosing thematics out of the topics listed above.

Here you can find the (tentative) programme
Alessandro's lecture notes about Hardy spaces can be found here
Moreover, here you can find Laura's slides Introduction to interpolation and the (hand written) notes
The collected notes of all the presentations of the seminar can be found in the following PDF (password protected)

• "Sobolev spaces" by R. A. Adams and J. F. Fournier (Academic Press, 2008)
• "Theory of function spaces" by H. Triebel (Birkhäuser, 1983)
• "Classical Fourier analysis" by L. Grafakos (Springer, 2014)
• "Modern Fourier analysis" by L. Grafakos (Springer, 2014)
• "Tools for PDE : pseudodifferential operators, paradifferential operators, and layer potentials" by M. E. Taylor, (American Mathematical Society , 2000)
• "Pseudodifferential Operators and Nonlinear PDE" by M. E. Taylor (Birkhäuser , 1991)
• "Interpolation spaces: an introduction" by J. Löfström and J. Bergh (Springer, 1976)
• "Singular integrals and differentiability properties of functions" by E. M. Stein (Princeton University Press , 1970)
• "Sobolev spaces of fractional order, Nemytskij operators, and nonlinear partial differential equations" by T. Runst and W. Sickel (De Gruyter, 1996)