Pointwise multipliers of Besov spaces on Carnot–Carathéodory spaces

Abstract

Let (X,d,μ) be a Carnot–Carathéodory space, namely, X 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 X satisfying that there exists constant C0∈[1,∞) such that for all x∈X and 0<r<diamX, μ(B(x,2r)):=μ({y∈X:d(x,y)<2r})≤C0μ(B(x,r))<∞(doublingproperty). Using the discrete Calderón reproducing formula and the Plancherel–Pôlya characterization of the inhomogeneous Besov spaces developed by Han et al. [12], and Han et al. (2008) [10], pointwise multipliers of inhomogeneous Besov spaces are obtained.