Séminaire Jeunes chercheurs (Khalid Baadi, jeudi 4 juin 2026)

La prochaine séance du séminaire Jeunes chercheurs du CEREMADE aura lieu le jeudi 4 juin 2026 à 17h en salle A707. Nous aurons le plaisir d'écouter Khalid Baadi (Laboratoires de mathématiques d'Orsay), qui nous parlera de

On the L^p boundedness of parabolic Riesz transforms with rough coefficients.

Abstract
In this talk, we present a necessary and sufficient condition for the $L^p$ boundedness, for p≤2, of parabolic Riesz transforms associated with parabolic operators whose elliptic part is in divergence form with rough coefficients (depending on space and time in a merely measurable way). This yields an extrapolation result from the case p=2 (the parabolic Kato square root estimate). Our approach relies on new off-diagonal estimates for the parabolic gradient of the resolvent family. These estimates exhibit weak decay, which is nevertheless sufficient for implementing a two-scale Blunck–Kunstmann extrapolation argument, yielding an extrapolation interval that can then be iterated to reach exponents strictly below $2_\star$. In the case of real coefficients, boundedness holds for all $p\in(1,2]$, together with a weak-type $(1,1)$ estimate for the spatial gradient component. We shall also discuss the case where the elliptic part is degenerate, in the presence of a Muckenhoupt weight. The talk is based on joint work with Moritz Egert and Benjamin Kosmala (TU Darmstadt, Germany).