$L^{p}-L^{q}$ theory for holomorphic functions of perturbed first order Dirac operators

Sebastian Stahlhut (1)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay

The aim of the article is to prove $L^{p}-L^{q}$ off-diagonal estimates and $L^{p}-L^{q}$ boundedness for operators in the functional calculus of certain perturbed first order differential operators of Dirac type for with $p\le q$ in a certain range of exponents. We describe the $L^{p}-L^{q}$ off-diagonal estimates and the $L^{p}-L^{q}$ boundedness in terms of the decay properties of the related holomorphic functions and give a necessary condition for $L^{p}-L^{q}$ boundedness. Applications to Hardy-Littlewood-Sobolev estimates for fractional operators will be given.

Mots clés: $L^{p}-L^{q}$ estimates; off-diagonal estimates; holomorphic functional calculus; First order differential operator; first order Dirac operator

Domaines: Analyse classique [math.CA]; Analyse fonctionnelle [math.FA]

Sebastian Stahlhut. $L^{p}-L^{q}$ theory for holomorphic functions of perturbed first order Dirac operators. Mémoires de la Société Mathématique de France, 2016, A priori estimates for boundary value elliptic problems via first order systems, 144. ⟨hal-00962253v2⟩