Sharp weighted $L^1$ bounds for Coulomb fields on the sphere

Evgueni Doubtsov, Ioann Vasilyev, Grigory Voinov

Let $d\ge 2$, let ${\alpha }_1,\dots ,{\alpha }_n>0$, and put $A={\sum }_k{\alpha }_k$. We determine, up to constants depending only on $d$, the smallest possible $L^1$ norm in the unit ball $\mathbb{B…