Abstract: We considered the problem of the sampling stability of function f in the Sobolev space subset V_α by means of sampling inequality，and gave the characterization condition of the sampling set X={x_j: j∈J}, which proved that the sampling inequality held under this condition, in other words, for any function f∈V_α could be stably reconstructed from the sample {f(x_j): j∈J}. Finally, the explicit expressions of the upper and lower bounds of the sampling inequality were given.

Key words: sampling inequality, Sobolev space, Poincaré inequality