  In this paper, we investigate the $L^{p}$ coarse Baum-Connes conjecture for
$p\in [1,\infty)$ via $C_{0}$ coarse structure, which is a refinement of the
bounded coarse structure on a metric space. We prove the $C_{0}$ version of the
$L^{p}$ coarse Baum-Connes conjecture and thus construct an obstruction group
for the conjecture. As an application, we show that the obstructions vanish
under the assumption of finite asymptotic dimension, and hence give a new proof
of the $L^{p}$ coarse Baum-Connes conjecture in this case.
