海森堡群上与分数次积分相关的交换子的有界性

The Boundedness of Commutators Associated with Fractional Integrals on the Heisenberg Group

令L=-ΔHn+V为海森堡群Hn上具有Gaussian核上界的Schrödinger算子,其中非负位势V属于逆Hölder类Bq,q≥Q/2。对于0-α/2为L的分数次积分算子。假设b属于比经典BMO型空间大的BMOρθ(Hn)空间。该文证明了交换子[b,L-α/2]从Lp1(Hn)到Lp2(Hn)是有界的,其中112 =1/p1-α/Q。

Let L=-ΔHn+V be the Schrödinger operator on Hn with Gaussian kernel bounds, where the nonnegative potential V belongs to the reverse Hölder class Bq, q≥Q/2. Let L-α/2 be the frac-tional integrals of L for 0ρθ(Hn), which is larger than classical BMOρθ(Hn). We obtain the boundedness of the commutator [b,L-α/2] from Lp1(Hn) to Lp2(Hn), where 112 =1/ p1-α/Q.