Let $p\in(1,\infty)$, $q\in[1,\infty)$, $s\in\mathbb{R}$ and $\tau\in[0,
1-\frac{1}{\max\{p,q\}}]$. In this paper, the authors establish the
$\phi$-transform characterizations of Besov-Hausdorff spaces $B{\dot
H}_{p,q}^{s,\tau}(\mathbb{R}^n)$ and Triebel-Lizorkin-Hausdorff spaces $F{\dot
H}_{p,q}^{s,\tau}(\mathbb{R}^n)$ ($q>1$); as applications, the authors then
establish their embedding properties (which on $B{\dot
H}_{p,q}^{s,\tau}(\mathbb{R}^n)$ is also sharp), smooth atomic and molecular
decomposition characterizations for suitable $\tau$.