The discrete maximal operator in metric spaces
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- Aalto, D. & Kinnunen, J. JAMA (2010) 111: 369. doi:10.1007/s11854-010-0022-3
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We study the action of the so-called discrete maximal operator on Newtonian, Hölder and BMO spaces on metric measure spaces equipped with a doubling measure and a Poincaré inequality. The discrete maximal operator has better regularity properties than the standard Hardy-Littlewood maximal operator and hence is a more flexible tool in this context.