Pointwise multipliers of Besov spaces on Carnot–Carathéodory spaces

Let (X,d,μ)(X,d,μ) be a Carnot–Carathéodory space, namely, XX is a smooth manifold, dd is a control, or Carnot–Carathéodory, metric induced by a collection of vector fields of finite type. μμ is a nonnegative Borel regular measure on XX satisfying that there exists constant C0∈[1,∞)C0∈[1,∞) such that for all x∈Xx∈X and 0