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I encounter the following problem: Let $f$ be a periodic continuous function in $[0,2\pi]$ such that the Fourier of $f$ is absolute convergence, that is $$|a_0|+\sum_{n=1}^\infty (|a_n|+|b_n|)<\infty,$$ where $f(x)\sim a_0+\sum_{n=1}^\infty (a_n\cos(nx)+b_n\sin(nx))$. Does $a_0+\sum_{n=1}^\infty (a_n\cos(nx)+b_n\sin(nx))$ converges uniformly on $[0,2\pi]$ to $f$? If the answer is affirmative, please give a reference. Thanks.

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