If u is a bivariate function and we have $\int_\theta^{\theta+1}{\int_\theta^y{u(x,y)(y-x)^{n-2}}dx}dy=0$ for all $\theta\in\mathbb R$, here $n>2$ is a constant, can we infer that $u=0$ a.e. on the area between two straight lines $y=x$ and $y=x+1$?
If yes, please give a proof; if no, please give a counterexample. Thanks!
PS: 1. This is not an exercise. 2. I have no idea about it.