# Gradient and Stability Estimates of Heat Kernels for Fractional Powers of Elliptic Operator

## TL;DR

This paper derives gradient and stability estimates for heat kernels related to fractional powers of elliptic operators, and also provides $L^p$-operator norm bounds for their semigroups, advancing understanding of fractional elliptic operators.

## Contribution

It introduces new gradient and stability estimates for heat kernels of fractional elliptic operators and establishes $L^p$-operator norm bounds for their semigroups.

## Key findings

- Gradient estimates for heat kernels of fractional elliptic operators
- Stability estimates for these heat kernels
- Bounds on $L^p$-operator norms of associated semigroups

## Abstract

Gradient and stability type estimates of heat kernel associated with fractional power of a uniformly elliptic operator are obtained. $L^p$-operator norm of semigroups associated with fractional power of two uniformly elliptic operators are also obtained.