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We study the linear wave equation □gu = 0 in Bondi-Sachs coordinates,for an asymptotically flat Lorentz metric g.We consider the null-timelike boundary problem,where an initial value is given on the null surface τ = 0 and a boundary value on the timelike surface r = ro.We obtain spacetime Hp-estimates of ru for r＞ro and derive an asymptotic expansion of ru in terms of 1/r as r →∞.