Maximal Operator in Variable Exponent Lebesgue Spaces on Unbounded Quasimetric Measure Spaces - Adamowicz, Tomasz; Harjulehto, Petteri; Hästö, Peter (MATHEMATICA SCANDINAVICA, 2015)
We study the Hardy-Littlewood maximal operator M on L^p(·)(X) when X is an unbounded (quasi)metric measure space, and p may be unbounded. We consider both the doubling and general measure case, and use two versions of the -Hölder condition. As a special case we obtain the criterion for a boundedness of M on L^p(·)(R^n,μ) for arbitrary, possibly non-doubling, Radon measures.