Dini–Lipschitz criterion
In mathematics, the Dini–Lipschitz criterion is a sufficient condition for the Fourier series of a periodic function to converge uniformly at all real numbers. It was introduced by , as a strengthening of a weaker criterion introduced by . The criterion states that the Fourier series of a periodic function f converges uniformly on the real line if 

where  is the modulus of continuity of f with respect to .

References

Fourier series
Theorems in Fourier analysis