  We consider the non-cutoff Boltzmann equation in the spatially inhomogeneous,
soft potentials regime, and establish decay estimates for large velocity. In
particular, we prove that pointwise algebraically decaying upper bounds in the
velocity variable are propagated forward in time whenever the solution has
finite weighted $L^\infty_{t,x} L^p_v$-norms for certain $p$. The main novelty
is that these estimates hold for any decay exponent above $\max\{2,3 + \gamma\}
+2s$, where $\gamma$ and $s$ are standard physical parameters such that $\gamma
\in (-3,0)$ and $s\in (0,1)$. Our results are useful even for solutions with
mild decay.
  As an application, we combine our decay estimates with recent short-time
existence results to derive a continuation criterion for large-data solutions.
Compared to past results, this extends the range of allowable parameters and
weakens the requirements on smoothness and decay in velocity of solutions.
