Hörmander Functional Calculus for Poisson Estimates - Archive ouverte HAL Access content directly
Journal Articles Integral Equations and Operator Theory Year : 2014

Hörmander Functional Calculus for Poisson Estimates


The aim of the article is to show a Hörmander spectral multiplier theorem for an operator $A$ whose kernel of the semigroup $\exp(-zA)$ satisfies certain Poisson estimates for complex times $z.$ Here $\exp(-zA)$ acts on $L^p(\Omega),\,1 < p < \infty,$ where $\Omega$ is a space of homogeneous type with the additional condition that the measure of annuli is controlled. In most of the known Hörmander type theorems in the literature, Gaussian bounds and self-adjointness for the semigroup are needed, whereas here the new feature is that the assumptions are the to some extend weaker Poisson bounds, and $\HI$ calculus in place of self-adjointness. The order of derivation in our Hörmander multiplier result is typically $\frac{d}{2},$ $d$ being the dimension of the space $\Omega.$ Moreover the functional calculus resulting from our Hörmander theorem is shown to be $R$-bounded. Finally, the result is applied to some examples.
Fichier principal
Vignette du fichier
Poisson.pdf (337.55 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-00794258 , version 1 (25-02-2013)
hal-00794258 , version 2 (09-04-2014)
hal-00794258 , version 3 (23-10-2018)



Christoph Kriegler. Hörmander Functional Calculus for Poisson Estimates. Integral Equations and Operator Theory, 2014, 80 (3), pp.379-413. ⟨hal-00794258v3⟩
314 View
272 Download



Gmail Facebook Twitter LinkedIn More