Transference of weak type bounds of multiparameter ergodic and geometric maximal operators
Transference of weak type bounds of multiparameter ergodic and geometric maximal operators
复制标题
多参数遍历和几何极大算子的弱类型界限的传递
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
A. Stokolos
中科院分区：
文献类型：
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作者：
P. Hagelstein;A. Stokolos
令U1，. . .，Ud是概率空间（Ω，Ω，μ）上保交换测度变换的非周期集合.设Γ是Z+的非空子集，B是R中边平行于轴的长方体的相关集合，其维数为n1 × ··· × nd，其中（n1，. . .，nd）∈ Γ.相关的多参数几何和各态历经极大算子MB和MΓ分别在L（R）和L（Ω）上定义为MBg（x）= sup x∈R∈B 1| R| R| g（y）|dy和MΓ f（ω）= sup（n1，.，nd）∈Γ 1 n1 · · ·nd n1−1 ∑
Let U1, . . . , Ud be a non-periodic collection of commuting measure preserving transformations on a probability space (Ω,Σ, μ). Also let Γ be a nonempty subset of Z+ and B the associated collection of rectangular parallelepipeds in R with sides parallel to the axes and dimensions of the form n1 × · · · × nd with (n1, . . . , nd) ∈ Γ. The associated multiparameter geometric and ergodic maximal operators MB and MΓ are defined respectively on L(R) and L(Ω) by MBg(x) = sup x∈R∈B 1 |R| R |g(y)| dy and MΓ f(ω) = sup (n1,...,nd)∈Γ 1 n1 · · ·nd n1−1 ∑