$\ell^p$-coarse Baum-Connes conjecture for $\ell^{q}$-coarse embeddable spaces

We prove an $\ell^p$-version of the coarse Baum-Connes conjecture for spaces that coarsely embedds into $\ell^q$-spaces for any $p$ and $q$ in $[1,\infty)$.