Riesz potentials in Besov and Triebel-Lizorkin spaces over spaces of homogeneous type

摘要

By using the discrete Calderon reproducing formulae, the author first establishes the boundedness of the Riesz-potential-type operator in homogeneous Besov and Triebel-Lizorkin spaces over spaces of homogeneous type. Then, by use of the T1 theorems for these spaces, the author proves that this operator of Riesz potential type can be used as the lifting operator of these spaces. [References: 20]