A necessary condition for the boundedness of the maximal operator on $L^{p(\cdot )}$ over reverse doubling spaces of homogeneous type

Oleksiy Karlovych, Alina Shalukhina

Let $(X,d,\mu )$ be a space of homogeneous type and $p(\cdot ):X\to [1,\infty ]$ be a variable exponent. We show that if the measure $\mu$ is Borel-semiregular and reverse doubling, then t…