Sharp reversed Hardy-Littlewood-Sobolev inequality on R^n

TitleSharp reversed Hardy-Littlewood-Sobolev inequality on R^n
Publication TypeJournal Article
Year of Publication2017
AuthorsNgô, QAnh, Nguyen, VH
JournalIsrael Journal of Mathematics
Volume220
Issue1
Pagination189-223
Abstract

This is the first in our series of papers that concerns Hardy-Littlewood-Sobolev (HLS) type inequalities. In this paper, the main objective is to establish the following sharp reversed HLS inequality in the whole space Rn
RnRnf(x)|xy|λg(y)dxdyCn,p,rfLp(Rn)gLr(Rn)for any non-negative functions fLp(Rn), gLr(Rn), and p,r(0,1), λ>0 such that 1/p+1/rλ/n=2. We will also explore some estimates for Cn,p,r and the existence of optimal functions for the above inequality, which will shed light on some existing results in literature.

URLhttp://dx.doi.org/10.1007/s11856-017-1515-x
DOI10.1007/s11856-017-1515-x