二维p-级数域上二进求导极大算子

摘要

In this paper,we consider the maximal operator of dyadic derivative on p series field.By using property of Dirichlet kernel,we construct a counter-example to prove that the oneand two-dimensional maximal operators are not bounded from Hardy space Hq to Hardy space Hq for 0 ＜ q ≤ 1.These results enrich some known conclusions on Walsh groups.%本文研究二维情况下p-级数域上二进求导极大算子的有界性.利用狄利克雷核的重要性质,构造反例证明此极大算子不是从Hardy空间Hq到Hardy空间Hq有界的,其中0＜q≤1.此结果完善了Walsh群上的已有结论.