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The square variation of rearranged Fourier series
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 137, Number 5, October 2015
- pp. 1257-1291
- 10.1353/ajm.2015.0032
- Article
- Additional Information
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 $O_{\epsilon}(\log^{9/22+\epsilon}(N))$. This is an improvement over $O(\log^{1/2}(N))$ from the canonical ordering.