Abstract
We prove that the Hardy-Littlewood maximal operator is bounded in the Sobolev spaceW 1,p(R n) for 1<p≤∞. As an application we study a weak type inequality for the Sobolev capacity. We also prove that the Hardy-Littlewood maximal function of a Sobolev function is quasi-continuous.
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Kinnunen, J. The hardy-littlewood maximal function of a sobolev function. Isr. J. Math. 100, 117–124 (1997). https://doi.org/10.1007/BF02773636
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DOI: https://doi.org/10.1007/BF02773636