与高阶抛物型Schrdinger算子相关的Riesz变换的L^p估计

The L^p estimates of Riesz transform associated with higher-order parabolic Schrdinger operator

令δδt+(-△)2+V2为Rn+1(n 5)上的高阶抛物型Schrdinger算子,其中非负位势V与时间t无关且属于逆Hlder类Bq1(Rn)(q1>n/2).本文得到与高阶抛物型Schrdinger算子相关的Riesz变换▽2(δδt+(-△)2+V2)-12的Lp(Rn+1)估计.

Let δ/δt＋（-△）^2＋V^2 be the higher-order parabolic Schrodinger operators on R^n＋1 （n≥5）, where the non-negative potential V is independent of t and belongs to the reverse Holder class Bq1 （R^n） （q1 〉 n/2）. In this paper, we obtain the L^p（R^n＋1） estimates of Riesz transform ▽^2（δ/δt＋（-△）^2＋V^2）^-1/2 associated with higher-order parabolic Schrodinger operators.