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
DOI: 10.12677/PM.2020.1010108, PDF,    科研立项经费支持
作者: 高春芳：青岛大学数学与统计学院，山东 青岛
关键词: 海森堡群；Gaussian上界；交换子；新BMO函数；Heisenberg Group； Gaussian Bound； Commutator； New BMO Function
摘要: 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< Q，令L-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1< p1< Q/α，1/ p2 =1/p1-α/Q。
Abstract: 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 0< α< Q. Suppose b∈BMOρθ(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 1< p1< Q/α, 1/ p2 =1/ p1-α/Q.
文章引用：高春芳. 海森堡群上与分数次积分相关的交换子的有界性[J]. 理论数学, 2020, 10(10): 928-937. https://doi.org/10.12677/PM.2020.1010108

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