%0 Journal Article
%T $L^{p}-L^{q}$ theory for holomorphic functions of perturbed first order Dirac operators
%A Sebastian Stahlhut
%J Mathematics
%D 2014
%I arXiv
%X 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.
%U http://arxiv.org/abs/1403.5368v2