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arXiv · 2512.06821

Representation of quasi-periodic functions and Hausdorff-Young inequalities for Besicovitch almost periodic functions

Aihua Fan·Kai Jiang·Pingwen Zhang
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Abstract

For a class of $\mathbb{R}^d$-ations and $\mathbb{Z}^d$-actions on the $n$-dimensional torus $\mathbb{T}^n$, we characterize their unique ergodicity and establish a theorem of Weyl type. This result allows us to establish an isomorphism between the Banach algebra of quasi-periodic functions with spectrum in a given $\mathbb{Z}$-module and the Banach algebra of periodic functions on a torus. This, in return, allows us to give a very simple proof of Hausdorff-Young inequalities for Besicovitch almost periodic functions. The regularity of the parent function of a quasi-periodic function is also studied.

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Aihua Fan, Kai Jiang, Pingwen Zhang. 2025-12-07. Representation of quasi-periodic functions and Hausdorff-Young inequalities for Besicovitch almost periodic functions. https://arxiv.org/abs/2512.06821

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