We obtain a global fractional Calder on-Zygmund type regularity theory for the fractional Poisson problem. More precisely, for
RN, N > 2, a bounded domain with boundary @
of class C2, s 2 (0; 1)
and f 2 Lm(
) for some m > 1, we consider the problem
( )su = f in
; u = 0 in RN n
;and, according to m, we nd the values of s 6 t < minf1; 2sg and of 1 < p < +1 such that u 2 Lt;p(RN)
and such that u 2 Wt;p(RN).