Abstract
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.
Highlights
The multiplier theory of function spaces has been studied for a long time, and a lot of results have been obtained
It was not clear how to generalize the pointwise multipliers on Rn to spaces of homogeneous type introduced by Coifman and Weiss see 9 because the Fourier transform is no longer available
We always assume that X, d is a metric space with a regular Borel measure μ such that all balls Journal of Function Spaces and Applications defined by d have finite and positive measures
Summary
The multiplier theory of function spaces has been studied for a long time, and a lot of results have been obtained.
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