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Abstract and Applied Analysis
Volume 2012, Article ID 583156, 23 pages
http://dx.doi.org/10.1155/2012/583156
Research Article

Carleson Measure and Tent Spaces on the Siegel Upper Half Space

College of Mathematics, Qingdao University, Qingdao 266071, China

Received 22 April 2012; Accepted 31 October 2012

Academic Editor: Natig Atakishiyev

Copyright © 2012 Kai Zhao. 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

The Hausdorff capacity on the Heisenberg group is introduced. The Choquet integrals with respect to the Hausdorff capacity on the Heisenberg group are defined. Then the fractional Carleson measures on the Siegel upper half space are discussed. Some characterized results and the dual of the fractional Carleson measures on the Siegel upper half space are studied. Therefore, the tent spaces on the Siegel upper half space in terms of the Choquet integrals are introduced and investigated. The atomic decomposition and the dual spaces of the tent spaces are obtained at the last.