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I want to know if there is a simple proof of the almost everywhere convergence of the Fourier series of a function in $C(\mathbb{T})$. I am aware of Carleson-Hunt Theorem. I was wondering if the proof simplifies for functions in $C(\mathbb{T})$.

Thank you.

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  • $\begingroup$ My guess is it doesn't. For example, $f\in C(T)$ gives no better decay of the Fourier coefficients than $f\in L^2(T)$. $\endgroup$
    – Christian Remling
    Commented Nov 22, 2023 at 22:33

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