In this note we show that the local Hardy-Littlewood maximal operator is bounded in the Sobolev space. Thus the maximal function often has partial derivatives. We also show that the maximal operator preserves the zero boundary values in Sobolev's sense.
|Number of pages||7|
|Journal||JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK|
|Publication status||Published - 1998|
|MoE publication type||A1 Journal article-refereed|