The nonlocal isoperimetric problem for polygons: Hardy-Littlewood and Riesz inequalities

Beniamin Bogosel, Dorin Bucur, Ilaria Fragalà

Given a non-increasing and radially symmetric kernel in $L_{\mathrm{loc}}^1({\mathbb{R}}^2;{\mathbb{R}}_{+})$, we investigate counterparts of the classical Hardy-Littlewood and Riesz inequa…