Hörmander Type Functional Calculus and Square Function Estimates

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-00662259
Contributeur : Christoph Kriegler <>
Soumis le : lundi 23 janvier 2012 - 15:43:07
Dernière modification le : lundi 23 janvier 2012 - 20:34:54
Document(s) archivé(s) le : mardi 24 avril 2012 - 02:25:43

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  • HAL Id : hal-00662259, version 1
  • ARXIV : 1201.4830

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Christoph Kriegler. Hörmander Type Functional Calculus and Square Function Estimates. 2012. 〈hal-00662259〉

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