Non-local Gehring Lemmas in Spaces of Homogeneous Type and Applications

@article{Auscher2019NonlocalGL,
  title={Non-local Gehring Lemmas in Spaces of Homogeneous Type and Applications},
  author={Pascal Auscher and Simon Bortz and Moritz Egert and Olli Saari},
  journal={The Journal of Geometric Analysis},
  year={2019},
  pages={1-46}
}
We prove a self-improving property for reverse Hölder inequalities with non-local right-hand side. We attempt to cover all the most important situations that one encounters when studying elliptic and parabolic partial differential equations. We present applications to non-local extensions of $$A_{\infty }$$A∞ weights and fractional elliptic divergence form equations. We write our results in spaces of homogeneous type. 
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