Sharp pointwise gradient estimates for Riesz potentials with a bounded density

TL;DR

This paper derives precise pointwise inequalities for Riesz potentials and their gradients in Euclidean space, enhancing tools for potential analysis and related mathematical fields.

Contribution

It introduces sharp pointwise inequalities for Riesz potentials and their gradients, advancing theoretical understanding and applications in potential analysis.

Findings

Established sharp pointwise inequalities for Riesz potentials.

Demonstrated usefulness in potential analysis and moment theory.

Provided tools for further mathematical research in related areas.

Abstract

We establish sharp pointwise inequalities for the Riesz potential and its gradient in $\mathbb{R}^{n}$ and indicate their usefulness for potential analysis, moment theory and other applications.