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

Let be a Carnot-Carathéodory space, namely, is a smooth manifold, is a control, or Carnot-Carathéodory, metric induced by a collection of vector fields of finite type. is a nonnegative Borel regular measure on satisfying that there exists constant such that for all and  diam , . 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.