$L^p$ Coarse Baum-Connes Conjecture and $K$-theory for $L^p$ Roe Algebras

In this paper, we verify the $L^p$ coarse Baum-Connes conjecture for spaces with finite asymptotic dimension for $p\in [1,\mathrm{\infty })$. We also show that the $K$-theory of $L^p$ Roe algebras are independent of $p\in (1,\mathrm{\infty })$ for spaces with finite asymptotic dimension.