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# Weighted Carleson Measure Spaces Associated with Different Homogeneities

Published:2013-07-16
Printed: Dec 2014
• Xinfeng Wu,
Department of Mathematics, China University of Mining and Technology (Beijing), Beijing 100083, China
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## Abstract

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.
 Keywords: composition of operators, weighted Carleson measure spaces, duality
 MSC Classifications: 42B20 - Singular and oscillatory integrals (Calderon-Zygmund, etc.) 42B35 - Function spaces arising in harmonic analysis