2维二进求导极大算子的有界性

摘要

本文研究了二进求导极大算子的有界性.利用狄利克雷核的重要性质,构造了反例证明此极大算子在一维和二维情况下都不是从Hardy空间Hn到Hardy空间Hp有界的,其中0＜p≤1.此结果说明文献[4]中的结论是不正确的.%In this paper, we consider the maximal operator of dyadic derivative. By using property of Dirichlet kernel, we construct a counter-example to prove that the one- and two-dimensional maximal operators are not bounded from the Hardy space Hp to the Hardy space Hp for 0 ＜ p ≤ 1. These results enrich some known conclusions and point out that the conclusion in[4] is incorrect.