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On UC-multipliers for multiple trigonometric systems
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We investigate the class of sequences $w(n)$ that can serve as almost-everywhere convergence Weyl multipliers for all rearrangements of multiple trigonometric systems. We show that any such sequence must satisfy the bounds $\log n\lesssim w(n)\lesssim\log^2 n$. Our main result establishes a general equivalence principle between one-dimensional and multidimensional trigonometric systems, which allows one to extend certain estimates known for the one-dimensional case to higher dimensions.
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Cited by 1 Pith paper
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Quantitative estimates for the absolute convergence of wavelet-type series
The sum 1/(n w(n)) converging is necessary and sufficient for an increasing w(n) to be an a.e. unconditional convergence Weyl multiplier for arbitrary wavelet-type systems, and log n is optimal for rearranged systems.
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