Lp estimates for higher-order parabolic Schr?dinger operators with certain nonnegative potentials

Let ?/?t + (??) 2 +V 2 be a higher order parabolic Schrodinger operator on ¨ R n+1 (n ? 5), where the nonnegative potentialV belongs to the reverse Holder class ¨ Bq 1 (R n ) for some q1 > n/2. In this paper we obtain the L p (R n+1 ) estimates for the operator ? 4 (?/?t+ (??) 2 +V 2 ) ?1 .