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∞ weights and fractional elliptic divergence form equations. We write our results in spaces of homogeneous type.
- (non-local) Reverse Hölder inequalities
- (very weak) A weights
- C weights
- Fractional elliptic equations
- Gehring’s lemma
- Self-improvement properties
- Spaces of homogeneous type