In this paper, we introduce weighted Carleson measure spaces associated
with different homogeneities and prove that these spaces are the dual spaces
of weighted Hardy spaces studied in a forthcoming paper.
As an application, we establish
the boundedness of composition of two Calderón-Zygmund operators with
different homogeneities on the weighted Carleson measure spaces; this,
in particular, provides the weighted endpoint estimates for the operators
studied by Phong-Stein.
composition of operators, weighted Carleson measure spaces, duality
42B20 - Singular and oscillatory integrals (Calderon-Zygmund, etc.)
42B35 - Function spaces arising in harmonic analysis