# American Institute of Mathematical Sciences

2005, 2005(Special): 164-172. doi: 10.3934/proc.2005.2005.164

## Weighted Hardy-Littlewood-Sobolev inequalities and systems of integral equations

 1 Department of Mathematics, Yeshiva University, New York, NY 10033 2 Department of Applied Mathematics, University of Colorado at Boulder, United States 3 Department of Applied Mathematics, University of Colorado at Boulder, Campus Box 526, Boulder, CO 80309-0526, United States

Received  September 2004 Revised  February 2005 Published  September 2005

In this paper, we consider systems of integral equations related to the weighted Hardy-Littlewood-Sobolev inequality. We present the symmetry, monotonity, and regularity of the solutions. In particular, we obtain the optimal integrability of the solutions to a class of such systems. We also present a simple method for the study of regularity, which has been extensively used in various forms. The version we present here contains some new developments. It is much more general and very easy to use. We believe the method will be helpful to both experts and non-experts in the field.
Citation: Wenxiong Chen, Chao Jin, Congming Li, Jisun Lim. Weighted Hardy-Littlewood-Sobolev inequalities and systems of integral equations. Conference Publications, 2005, 2005 (Special) : 164-172. doi: 10.3934/proc.2005.2005.164
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