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

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