Hardy's Inequality for the fractional powers of Grushin operator

TL;DR

This paper establishes Hardy's inequality for fractional powers of the Grushin operator and generalized sublaplacian, providing integral and ground state representations for these fractional powers.

Contribution

It introduces Hardy's inequality for fractional powers of the Grushin operator and generalized sublaplacian, along with new integral and ground state representations.

Findings

Hardy's inequality proven for fractional powers of the Grushin operator

Integral representation for fractional powers derived

Ground state representation established

Abstract

We prove Hardy's inequality for the fractional powers of the generalized sublaplacian and the fractional powers of the Grushin operator. We also find an integral representation and a ground state representation for the fractional powers of generalized sublaplacian.