# 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.

## 6 Citations

A note on generalized Fujii-Wilson conditions and BMO spaces

- Mathematics
- 2019

In this note we generalize the definition of the Fujii-Wilson condition providing quantitative characterizations of some interesting classes of weights, such as A ∞ , A ∞ weak and C p , in terms of…

$$\mathrm {L}^p$$-extrapolation of non-local operators: Maximal regularity of elliptic integrodifferential operators with measurable coefficients

- Mathematics
- 2020

The aim of this article is to deepen the understanding of the derivation of $\mathrm{L}^p$-estimates of non-local operators. We review the $\mathrm{L}^p$-extrapolation theorem of Shen which builds on…

$C_p$ estimates for rough homogeneous singular integrals and sparse forms

- Mathematics
- 2019

We consider Coifman--Fefferman inequalities for rough homogeneous singular integrals $T_\Omega$ and $C_p$ weights. It was recently shown by Li-Perez-Rivera-Rios-Roncal that $$
\|T_\Omega \|_{L^p(w)}…

Calderon-Zygmund type estimates for nonlocal PDE with Hölder continuous kernel

- MathematicsAdvances in Mathematics
- 2021

Sharp Reverse Hölder Inequality for
$$C_p$$
C
p
Weights and Applications

- Mathematics
- 2020

We prove an appropriate sharp quantitative reverse Hölder inequality for the $$C_p$$ C p class of weights from which we obtain as a limiting case the sharp reverse Hölder inequality for the…

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