An $L^1$-type estimate for Riesz potentials

Armin Schikorra, Daniel Spector, Jean Van Schaftingen

In this paper we establish new $L^1$-type estimates for the classical Riesz potentials of order $\alpha \in (0,N)$: \[ \|I_αu\|_{L^{N/(N-α)}(\mathbb{R}^N)} \leq C \|Ru\|_{L^1(\mathbb{R}…