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Local real analysis in locally homogeneous spaces

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Abstract

We introduce the concept of locally homogeneous space, and prove in this context L p and C α 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.

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Authors and Affiliations

  1. Dipartimento di Matematica, Politecnico di Milano, Via Bonardi 9, 20133, Milano, Italy

    Marco Bramanti

  2. Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an, 710129, Shaanxi, China

    Maochun Zhu

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  1. Marco Bramanti
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  2. Maochun Zhu
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Correspondence to Maochun Zhu.

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Bramanti, M., Zhu, M. Local real analysis in locally homogeneous spaces. manuscripta math. 138, 477–528 (2012). https://doi.org/10.1007/s00229-011-0501-6

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