Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 731016, 21 pages
doi:10.1155/2010/731016
Research Article

Multilinear Riesz Potential on Morrey-Herz Spaces with Non-Doubling Measures

Yanlong Shi,1 Xiangxing Tao,2 and Taotao Zheng3

1Department of Fundamental Courses, Zhejiang Pharmaceutical College, Ningbo, Zhejiang 315100, China
2Department of Mathematics, Zhejiang University of Science & Technology, Hangzhou, Zhejiang 310023, China
3Department of Mathematics, Ningbo University, Ningbo, Zhejiang 315211, China

Received 19 November 2009; Accepted 10 March 2010

Academic Editor: Nikolaos Papageorgiou

Copyright © 2010 Yanlong Shi et al. 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 authors consider the multilinear Riesz potential operator defined by ℐα,m(f⃗)(x)=∫(ℝd)m(f1(y1)f2(y2)⋯fm(ym)/|(x-y1,…,x-ym)|mn-α)dμ(y1)⋯dμ(ym), where f⃗ denotes the m-tuple (f1,f2,…,fm), m,n the nonnegative integers with n≥2, m≥1, 0<α<mn, and μ is a nonnegative n-dimensional Borel measure. In this paper, the boundedness for the operator ℐα,m on the product of homogeneous Morrey-Herz spaces in nonhomogeneous setting is found.