Pointwise Multipliers of Triebel-Lizorkin Spaces on Carnot-Carathéodory Spaces

摘要

Let(𝒳,d,μ)be a Carnot-Carathéodory space, namely,𝒳is a smooth manifold,dis a control, or Carnot-Carathéodory, metric induced by a collection of vector fields of finite type.μis a nonnegative Borel regular measure on𝒳satisfying that there exists constantC0∈[1,∞)such that for allx∈𝒳and0<r< diam 𝒳,μ(B(x,2r)):=μ({y∈𝒳:d(x,y)<2r})≤C0μ(B(x,r))<∞ (doubling property). Using the discrete Calderón reproducing formula and the Plancherel-Pôlya characterization of the inhomogeneous Triebel-Lizorkin spaces developed in Han et al., in press and Han et al., 2008, pointwise multipliers of inhomogeneous Triebel-Lizorkin spaces are obtained.