Maximal operators associated to discrete subgroups of nilpotent Lie groups
Maximal operators associated to discrete subgroups of nilpotent Lie groups
复制标题
与幂零李群的离散子群相关的最大算子
DOI：
10.1007/s11854-007-0010-4
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
S. Wainger
中科院分区：
文献类型：
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作者：
Á. Magyar;E. Stein;S. Wainger
本文的目的是证明幂零李群的合适离散子簇上取均值的极大定理。这个结果最简单的例子出现在3 × 3严格上三角矩阵群（Heisenberg群，h1）上。在这个例子中，我们考虑由（1.1）给出的定义在z3上的函数f的平均值：A r (f)(A) = 1 r 2 b=(b1, b2)∈z2 |b|<r f (a1 + b1, a2 + b2, a3 + a1 b2)，其中A =(a1, a2, a3)∈z3。
The purpose of this paper is to prove a maximal theorem for averages taken over suitable discrete sub-varieties of nilpotent Lie groups. The simplest instance of this result arises for the group of 3 × 3 strictly upper-triangular matrices, (the Heisenberg group, H 1). In this example one considers averages for functions f defined on Z 3 given by (1.1) A r (f)(a) = 1 r 2 b=(b 1 ,b 2)∈Z 2 |b|<r f (a 1 + b 1 , a 2 + b 2 , a 3 + a 1 b 2), with a = (a 1 , a 2 , a 3) ∈ Z 3 .