The hardy-littlewood maximal function of a sobolev function
- Cite this article as:
- Kinnunen, J. Isr. J. Math. (1997) 100: 117. doi:10.1007/BF02773636
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We prove that the Hardy-Littlewood maximal operator is bounded in the Sobolev spaceW1,p(Rn) 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.