Weak A∞ weights and weak Reverse Hölder property in a space of homogeneous type

الأصل · EN

In the Euclidean setting, the Fujii-Wilson-type A∞ weights satisfy a Reverse Hölder Inequality (RHI) but in spaces of homogeneous type the best known result has been that A∞ weights satisfy only a weak Reverse Hölder Inequality. In this paper, we compliment the results of Hytönen, Pérez and Rela and show that there exist both A∞ weights that do not satisfy an RHI and a genuinely weaker weight class that still satisfies a weak RHI. We also show that all the weights that satisfy a weak RHI have a self-improving property but the self-improving property of the strong Reverse Hölder weights fails in a general space of homogeneous type. We prove most of these purely non-dyadic results using convenient dyadic systems and techniques.