Local real analysis in locally homogeneous spaces

• DOI: 10.1007/s00229-011-0501-6
• Publication Date: 2011-11-08T08:32:47Z
• Authors: Marco Bramanti; Maochun Zhu
• Keywords: Commutator; Homogeneous function

We introduce the concept of locally homogeneous space, and prove in this context L^p and Holder estimates for singular and fractional integrals, as well as L^p estimates on the commutator of a singular or fractional integral with a BMO or VMO function. These results are motivated by local a-priori estimates for subelliptic equations.