  In this paper, we consider the perturbed solutions with polynomial tail in
large velocities for the non-cutoff Boltzmann equation near global Maxwellians
in the whole space. The global in time existence is proved in the weighted
Sobolev spaces and the almost optimal time decay is obtained in Fourier
transform based low-regularity spaces. The result shows a time-velocity decay
structure of solutions that can be decomposed into two parts. One part allows
the slow polynomial tail in large velocities, carries the initial data and
enjoys the exponential or arbitrarily large polynomial time decay. The other
part, with zero initial data, is dominated by the non-negative definite
symmetric dissipation and has the exponential velocity decay but only the slow
polynomial time decay.
