  We extend some classical results of Cowling and Meda to the noncommutative
setting. Let $(T_t)_{t>0}$ be a symmetric contraction semigroup on a
noncommutative space $L_p(\mathcal{M}),$ and let the functions $\phi$ and
$\psi$ be regularly related. We prove that the semigroup $(T_t)_{t>0}$ is
$\phi$-ultracontractive, i.e. $\|T_t x\|_\infty \leq C \phi(t)^{-1} \|x\|_1$
for all $x\in L_1(\mathcal{M})$ and $ t>0$ if and only if its infinitesimal
generator $L$ has the Sobolev embedding properties: $\|\psi(L)^{-\alpha} x\|_q
\leq C'\|x\|_p$ for all $x\in L_p(\mathcal{M}),$ where $1<p<q<\infty$ and
$\alpha =\frac{1}{p}-\frac{1}{q}.$ We establish some noncommutative spectral
multiplier theorems and maximal function estimates for generator of
$\phi$-ultracontractive semigroup. We also show the equivalence between
$\phi$-ultracontractivity and logarithmic Sobolev inequality for some special
$\phi$. Finally, we gives some results on local ultracontractivity.
