A remark on estimates for uniformly elliptic operators on weighted L-p spaces and Morrey spaces

In this paper we consider uniformly elliptic operators L = - Sigma(i,j=1) ( n) delta(i) (a(ij) (x)delta(j)) + V(x) with non-negative potentials V on R- n (n greater than or equal to 3) which belong to certain reverse Holder cla ss. We show several estimates for VL-1, V(1/2)del L-1 and del(2)L(-1) on we ighted L-p spaces and Morrey spaces under certain assumptions on a(ij)(x), V and p. Our results generalize some results of J. ZHONG and Z. SHEN in the case of L = -Delta + V(x) and extend to uniformly elliptic operators.