Homogeneous algebras via heat kernel estimates

2021/02/23 by Bruno, Tommaso
#22E25 #43A85 #46F10 #58J35 #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Primary 46E35 #Secondary 46E36

paper · doi:10.48550/arxiv.2102.11613

Abstract

We study homogeneous Besov and Triebel--Lizorkin spaces defined on doubling metric measure spaces in terms of a self-adjoint operator whose heat kernel satisfies Gaussian estimates together with its derivatives. When the measure space is a smooth manifold and such operator is a sum of squares of smooth vector fields, we prove that their intersection with L^∞ is an algebra for pointwise multiplication. Our results apply to nilpotent Lie groups and Grushin settings.

Related

• Sobolev algebras through heat kernel estimates
• Heat kernel based decomposition of spaces of distributions in the framework of Dirichlet spaces
• Continuous characterizations of inhomogeneous Besov and Triebel-Lizorkin spaces associated to non-negative self-adjoint operators
• Grushin Operator on Infinite Dimensional Homogeneous Lie Groups
• Weighted Besov and Triebel--Lizorkin spaces associated to operators