# Coercivity estimates for integro-differential operators

## TL;DR

This paper establishes a general condition on the kernel of an integro-differential operator ensuring its quadratic form satisfies a coercivity estimate related to the $H^s$-seminorm, advancing understanding of such operators.

## Contribution

It introduces a broad condition on kernels that guarantees coercivity estimates for associated quadratic forms, extending previous results in integro-differential operator theory.

## Key findings

- Provides a new criterion for kernel coercivity
- Ensures quadratic forms are bounded below by the $H^s$-seminorm
- Enhances theoretical understanding of integro-differential operators

## Abstract

We provide a general condition on the kernel of an integro-differential operator so that its associated quadratic form satisfies a coercivity estimate with respect to the $H^s$-seminorm.