Abstract
The aim of this work is to investigate the integrability properties of the maximal operator Mµ, associated with a non-doubling measure µ defined on ℝn. We start by establishing for a wide class of radial and increasing measures µ, that Mµ is bounded on all the spaces Lµp(ℝn), p > 1. Also, we show that there is a radial and increasing measure µ for which Mµ does not map Lµp(ℝn) into weak Lµp(ℝn), 1 ≤ p < ∞.
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