Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 729824, 14 pages
doi:10.1155/2010/729824
Research Article

The Cauchy Integral Operator on the Predual of a Morrey Space

Jianmiao Ruan1,2 and Jiecheng Chen1

1Department of Mathematics, Zhejiang University, Hangzhou 310027, China
2Department of Mathematics, Zhejiang Education Institute, Hangzhou 310012, China

Received 15 November 2009; Accepted 5 March 2010

Academic Editor: Radu Precup

Copyright © 2010 Jianmiao Ruan and Jiecheng Chen. 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 show that the Cauchy integral operator is bounded from Hp,φ(R1) (the predual of a Morrey space) to hp,φ(R1) (the local version of Hp,φ(R1)). To prove our theorem we will introduce generalized atoms and consider a variant of “Tb theorem.”