与高阶抛物型Schrodinger算子相关的Riesz变换的L^p估计——献给陆善镇教授75华诞

令δ/δt＋（-△）^2＋V^2为R^n＋1（n≥5）上的高阶抛物型Schrodinger算子,其中非负位势V与时间t无关且属于逆Holder类Bq1（Rn）（q1〉n/2）.本文得到与高阶抛物型Schrodinger算子相关的Riesz变换▽^2（δ/δt＋（-△）^2＋V^2）^-1/2的L^p（R^n＋1）估计.

The Lp estimates of Riesz transform associated with higher-order parabolic Schrödinger operator

Let ?/?t + (-Δ)² + V ² be the higher-order parabolic Schrödinger operators on Rⁿ⁺¹ (n ≥ 5), where the non-negative potential V is independent of t and belongs to the reverse Hölder class B_q1 (Rⁿ) (q₁ > n=2). In this paper, we obtain the L^p(Rⁿ⁺¹) estimates of Riesz transform ?²(?/?t + (-Δ)² + V ²)^-1/2 associated with higher-order parabolic Schrödinger operators.