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

Abstract EN

Let (?,d,μ) be a Carnot-Carathéodory space, namely, ? is a smooth manifold, d is a control, or Carnot-Carathéodory, metric induced by a collection of vector fields of finite type.

μ is a nonnegative Borel regular measure on ? satisfying that there exists constant C0∈[1,∞) such that for all x∈? and 0

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.