arXiv subjects
Publications and source records attributed to L. Brandolini.
The classical Koksma Hlawka inequality does not apply to functions with simple discontinuities. Here we state a Koksma Hlawka type inequality which applies to piecewise smooth functions $fχ_Ω$, with $f$ smooth and $Ω$ a Borel subset of $[0,1]^{d}$.
We prove that the spherical mean of the Fourier transform of the characteristic function of a bounded convex set (without any additional assumptions) or a bounded set with a C^{3/2} boundary decays at infinity at the same rate as the Fourier transform of the characteristic function of the ball.