Calcul de Hörmander maximal et q-variationel
Christoph Kriegler
LMBP, Université Clermont Auvergne, Clermont-Ferrand
http://math.univ-bpclermont.fr/~kriegler/
Date(s) : 13/01/2020 iCal
10h00 - 11h00
Maximum and q-variational Hörmander calculus
The Hopf-Dunford-Schwartz theorem ensures that if (Tt)t≥0 is a Markovian semigroup (think of the heat semigroup) acting on the spaces Lp(Ω), 1 < p < ∞ then its contractivity on Lp(Ω) is reinforced in a maximal estimate ∥supt>0|Ttf|∥p ≤ Cp∥f∥p, which is a key estimate in classical harmonic analysis. In this talk we extend this result in several senses: Replace the hypotheses on the semigroup, consider spectral multipliers m (tA) more general than Tt = exp(–tA) (here therefore m(λ) = exp(–λ)) , look at the case of Bochner spaces Lp(Ω,ℓq) which includes estimations of square functions, and reinforce the quantity supt>0 by finer norms. This is a joint work with Luc Deléaval (University Paris-Est Marne-la-Vallée).
http://math.univ-bpclermont.fr/~kriegler/Maximal-Hoermander.pdf
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