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For a Lipschitz function $f$ defined in $[0,2\pi]^d$ for $d>1$, is that true that the multi-dimensional Fourier series converges absolutely? In other words, $\sum_{k\in \mathbb{Z}^d}|\hat{f}(k)|<\infty$. Is there any reference on such results?

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I found a related paper myself:

http://link.springer.com/article/10.1007%2Fs13324-012-0025-6

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