The logarithmic HLS inequality for systems on compact manifolds

We prove an optimal logarithmic Hardy–Littlewood–Sobolev inequality for systems on compact m-dimensional Riemannian manifolds, for any m 2. We show that a special case of the inequality, involving only two functions, implies the general case by using an argument from the theory of linear programing. © 2004 Elsevier Inc. All rights reserved.