Article Dans Une Revue Journal of Operator Theory Année : 2014

Hörmander Type Functional Calculus and Square Function Estimates

Résumé

We investigate Hörmander spectral multiplier theorems as they hold on $X = L^p(\Omega),\: 1 < p < \infty,$ for many self-adjoint elliptic differential operators $A$ including the standard Laplacian on $\R^d.$ A strengthened matricial extension is considered, which coincides with a completely bounded map between operator spaces in the case that $X$ is a Hilbert space. We show that the validity of the matricial Hörmander theorem can be characterized in terms of square function estimates for imaginary powers $A^{it}$, for resolvents $R(\lambda,A),$ and for the analytic semigroup $\exp(-zA).$ We deduce Hörmander spectral multiplier theorems for semigroups satisfying generalized Gaussian estimates.

Fichier principal
Vignette du fichier
Matricial.pdf (325.84 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Licence

Dates et versions

hal-00662259 , version 1 (23-01-2012)

Licence

Identifiants

Citer

Christoph Kriegler. Hörmander Type Functional Calculus and Square Function Estimates. Journal of Operator Theory, 2014, 71 (1), pp.223-257. ⟨hal-00662259⟩
282 Consultations
341 Téléchargements

Altmetric

Partager

  • More