Fractional operators and Sobolev spaces on homogeneous groups

TL;DR

This paper develops the theory of fractional operators on Lie groups of homogeneous type, establishing key properties and embedding theorems for related Sobolev spaces, advancing analysis on these structures.

Contribution

It introduces foundational properties of fractional operators on homogeneous Lie groups and proves embedding theorems for their Sobolev spaces, which was previously unexplored.

Findings

Established properties of fractional operators on homogeneous groups

Proved embedding theorems for Sobolev-type spaces on these groups

Extended analysis tools to a broader class of Lie groups

Abstract

We establish foundational properties of fractional operators on Lie groups of homogeneous type. We prove embedding theorems for the associated Sobolev-type spaces.