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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 thebounded 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 groupfor the conjecture. As an application, we show that the obstructions vanishunder the assumption of finite asymptotic dimension, and hence give a new proofof the $L^{p}$ coarse Baum-Connes conjecture in this case.

$L^p$ coarse Baum-Connes conjecture via $C_{0}$ coarse geometry