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Let u = u（t,x,p） satisfy the transport equation where f=f（t,x,p） belongs to L^p（（O,T） ×R^3×R^3） for 1 〈 p 〈 ∞ and is the relativistic-free transport operator from the relativistic Boltzmann equation. We show the regularity offR3 u（t, x, p）dp us