ar X iv : 0 90 5 . 31 11 v 2 [ m at h . D S ] 3 1 M ay 2 00 9 Relatively finite measure - preserving extensions and lifting multipliers by Rokhlin cocycles
نویسندگان
چکیده
We show that under some natural ergodicity assumptions extensions given by Rokhlin cocycles lift the multiplier property if the associated locally compact group extension has only countably many L ∞-eigenvalues. We make use of some analogs of basic results from the theory of finite-rank modules associated to an extension of measure-preserving systems in the setting of a non-singular base.
منابع مشابه
ar X iv : 0 90 5 . 31 11 v 1 [ m at h . D S ] 1 9 M ay 2 00 9 Relatively finite measure - preserving extensions and lifting multipliers by Rokhlin cocycles
We show that under some natural ergodicity assumptions extensions given by Rokhlin cocycles lift the multiplier property if the associated locally compact group extension has only countably many L ∞-eigenvalues. We make use of some analogs of basic results from the theory of finite-rank modules associated to an extension of measure-preserving systems in the setting of a non-singular base.
متن کامل2 3 Se p 20 09 Relatively finite measure - preserving extensions and lifting multipliers by Rokhlin cocycles
Dedicated to Stephen Smale in recognition of his contributions to topology and dynamical systems Abstract We show that under some natural ergodicity assumptions extensions given by Rokhlin cocycles lift the multiplier property if the associated locally compact group extension has only countably many L ∞-eigenvalues. We make use of some analogs of basic results from the theory of finite-rank mod...
متن کاملRelatively Finite Measure-preserving Extensions and Lifting Multipliers by Rokhlin Cocycles
Dedicated to Stephen Smale in recognition of his contributions to topology and dynamical systems Abstract We show that under some natural ergodicity assumptions extensions given by Rokhlin cocycles lift the multiplier property if the associated locally compact group extension has only countably many L ∞-eigenvalues. We make use of some analogs of basic results from the theory of finite-rank mod...
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Let h(y) be a bounded radial function and Ω (y ′) an H 1 function on the unit sphere satisfying the cancelation condition. Then the Marcinkiewicz integral operator µ Ω related to the Littlewood-Paley g−function is defined by µ Ω (f)(x) = ∞ 0 |F t (x)| 2 dt t 3 1 2 , (1) where F t (x) = |x−y|≤t Ω (x − y) |x − y| d−1 h (|x − y|) f (y)dy (2) and h(y) ∈ L ∞ (R +). In this paper, we prove that the o...
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تاریخ انتشار 2009