Optimal weak estimates for Riesz potentials

Abstract

In this note we prove a sharp reverse weak estimate for Riesz potentials \[ \Vert I_{s}(f)\Vert _{L^{\frac{n}{n-s},\infty }}\ge \gamma _sv_{n}^{\frac{n-s}{n}}\Vert f\Vert _{L^1}~\text{for}~0

Keywords

• Riesz potentials
• sharp constant
• optimal estimate