A good universal weight for multiple recurrence averages with commuting transformations in norm

Idris Assani; Ryo Moore

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arXiv · 1506.06730

A good universal weight for multiple recurrence averages with commuting transformations in norm

Idris Assani·Ryo Moore

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Abstract

We will show that the sequences appearing in Bourgain's double recurrence result are good universal weights to the multiple recurrence averages with commuting measure-preserving transformations in norm. This will extend the pointwise converge result of Bourgain, the norm convergence result of Tao, and the authors' previous work on the single measure-preserving transformation.

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Idris Assani, Ryo Moore. 2015-06-22. A good universal weight for multiple recurrence averages with commuting transformations in norm. https://arxiv.org/abs/1506.06730

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