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arXiv · 1212.1988

The Square Variation of Rearranged Fourier Series

Allison Lewko·Mark Lewko
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Abstract

We prove that there exists a rearrangement of the first $N$ elements of the trigonometric system such that the $L^2$-norm of the square variation operator is at most $O_ε(\log^{9/22+ε}(N))$. This is an improvement over $O(\log^{1/2}(N))$ from the canonical ordering.

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Allison Lewko, Mark Lewko. 2012-12-10. The Square Variation of Rearranged Fourier Series. https://arxiv.org/abs/1212.1988

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