Homogeneous algebras via heat kernel estimates

Bruno, Tommaso

doi:10.1090/tran/8697

Homogeneous algebras via heat kernel estimates
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Trans. Amer. Math. Soc. 375 (2022), 6903-6946 Request permission

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 $L^\infty$ is an algebra for pointwise multiplication. Our results apply to nilpotent Lie groups and Grushin settings.

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