Hi!

I need to find a 2pi-periodic function f:R->C, which is (Riemann) integrable on [-pi,pi] that satisfies the following properties:

1. the Fourier series of f is uniformly Cesaro summable for all x in [-pi,pi]

2. the Fourier series of f diverges for some x in [-pi,pi].

I mainly tried saw-tooth functions but they did not satisfy condition 1.

Thanks! :)