Grigory Voinov

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

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 $\mathbb{B}^d\subset \mathbb{R}^d$ of the Coulomb field generated by charges of strengths $\alpha_k$ placed on the unit sphere $\mathbb{S...