Affiliation:
1. Fachbereich Mathematik Technische Universität Darmstadt Darmstadt Germany
Abstract
AbstractWe give a simple argument to obtain ‐boundedness for heat semigroups associated to uniformly strongly elliptic systems on by using Stein interpolation between Gaussian estimates and hypercontractivity. Our results give explicitly in terms of ellipticity. It is optimal at the endpoint . We also obtain ‐estimates for the gradient of the semigroup, where depends on ellipticity but not on dimension.
Reference20 articles.
1. Vector-valued Laplace Transforms and Cauchy Problems
2. On necessary and sufficient conditions for Lp$L^p$‐estimates of Riesz transforms associated to elliptic operators on Rn$\mathbb {R}^n$ and related estimates;Auscher P.;Mem. Amer. Math. Soc.,2007
3. Regularity Theorems and Heat Kernel for Elliptic Operators
4. Boundary Value Problems and Hardy Spaces for Elliptic Systems with Block Structure
5. Astérisque;Auscher P.,1998