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

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?