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Abstract and Applied Analysis
Volume 2012, Article ID 879073, 26 pages
http://dx.doi.org/10.1155/2012/879073
Research Article

Generalized Carleson Measure Spaces and Their Applications

1Department of Mathematics, National Central University, Chung-Li 320, Taiwan
2Department of Applied Mathematics, National Dong Hwa University, Hualien 970, Taiwan

Received 10 October 2011; Revised 20 February 2012; Accepted 12 March 2012

Academic Editor: Stevo Stevic

Copyright © 2012 Chin-Cheng Lin and Kunchuan Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We introduce the generalized Carleson measure spaces CMOrα,q that extend BMO. Using Frazier and Jawerth's φ-transform and sequence spaces, we show that, for αR and 0<p1, the duals of homogeneous Triebel-Lizorkin spaces Ḟpα,q for 1<q< and 0<q1 are CMO(q'/p)-(q'/q)-α,q' and CMOr-α+(n/p)-n, (for any rR), respectively. As applications, we give the necessary and sufficient conditions for the boundedness of wavelet multipliers and paraproduct operators acting on homogeneous Triebel-Lizorkin spaces.