Weak type inequalities for ergodic strong maximal operators
Weak type inequalities for ergodic strong maximal operators
复制标题
遍历强极大算子的弱类型不等式
DOI：
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发表时间：
2010
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
Fava的弱L型对数L估计强两参数遍历极大算子对交换非周期测度保持变换被证明是尖锐的。此外，给定φ [0，∞）上的一个正的、递增的函数，且当x → ∞时为o（log（x）），以及有限测度空间Ω中的一对交换可逆的非周期保测度变换，构造了一个函数f ∈ L φ（L）（Ω），其相应的多参数遍历平均在无限制意义下几乎处处不收敛.
Fava’s weak type L log L estimate for strong two-parameter ergodic maximal operators associated to pairs of commuting non-periodic measure-preserving transformations is shown to be sharp. Moreover, given a function on φ [0, ∞) that is positive, increasing, and o (log( x )) for x → ∞ as well as a pair of commuting invertible non-periodic measure-preserving transformations n a space Ω of finite measure, a function f ∈ L φ( L )(Ω) is constructed whose associated multiparameter ergodic averages fail to converge almost everywhere in the unrestricted sense.