Abstract
Let \(\mathcal{E}(X,d,\mu)\) be a Banach function space over a space of homogeneous type \((X,d,\mu)\). We show that if the Hardy-Littlewood maximal operator \(M\) is bounded on the space \(\mathcal{E}(X,d,\mu)\), then its boundedness on the associate space \(\mathcal{E}'(X,d,\mu)\) is equivalent to a certain condition \(\mathcal{A}_\infty\). This result extends a theorem by Andrei Lerner from the Euclidean setting of \(\mathbb{R}^n\) to the setting of spaces of homogeneous type.
Citation
Alexei Yu. Karlovich. "Hardy-Littlewood Maximal Operator on the Associate Space of a Banach Function Space." Real Anal. Exchange 44 (1) 119 - 140, 2019. https://doi.org/10.14321/realanalexch.44.1.0119
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