The periodic Schrodinger operators with potentials in the Morrey class

We consider the periodic Schrodinger operator -Delta + V(x) in R-d, d greater than or equal to 3 with potential V in the Morrey class. Let 0 be a periodic cell for V. We show that, for p is an element of ((d - 1)/2, d/2], there exists a positive constant a depending only on the shape of [GRAPHICS] then the spectrum of -Delta + V is purely absolutely continuous. We obtain this result as a consequence of certain weighted L-2 Sobolev inequalities on the d-torus. It improves an early result by the author for potentials in L-d/2 or weak-L-d/2 space. (C) 2002 Elsevier Science (USA).