A Fourier series failing to converge on the Cantor Set This is a strengthening of Chandru's question:
Example of a function whose Fourier Series fails to converge at One point
Is there a nice and concrete example of a Fourier series that fails to converge on some "big" set of measure zero, for instance on the Cantor ternary set?

I don't have an exact answer for this but I think this paper might help:
Pointwise convergence of multiple Fourier series using different convergence notions

One more link:
In this paper the authors show that for any set of zero measure there exists a continuous function on the circle whose Fourier series diverges on that set. In French.
Sergei Vladimirovich Konyagin, On divergence of trigonometrique Fourier series everywhere, C. R. Acad. Sci. Paris 329 (1999), 693-697.
