与高阶Schrodinger型算子相关的变分算子的Lipschitz交换子

设L=(-Δ)²+V²是Rⁿ(n≥5)上的高阶Schrodinger型算子, 其中非负位势V属于反向Holder类RH_q(q>n/2). 记V_ρ(e^-tL)为与高阶Schrodinger型算子L相关的变分算子. 基于Herz型Hardy空间的原子分解理论, 利用Schrodinger型算子的性质, 证明该类变分算子与Lipschitz函数构成的交换子的L^q有界性, 并进一步证明该类变分算子的交换子从Herz型Hardy空间到Herz空间是有界的, 在Morrey-Herz空间上也是有界的.

Lipschitz Commutators of Variation Operators Associated with High Order Schrodinger Type Operators

Let L=(-Δ)²+V² be a high order Schrodinger type operator in Rⁿ (n≥5), where a nonnegative potential V belongs to the reverse Holder class RH_q(q>n/2). Let V_ρ(e^-tL) be the variation operator associated with the high order Schrodinger type operator L. Based on the theory of atomic decompesitions of Herz type Hardy spaces, by using the properties of the Schrodinger type operators, the boundedness of the commutators composed by such variation operators and Lipschitz fuctions on L^q is proved. Furthermore, it is proved that the commutators of this kind of variation operators are bounded from Herz type Hardy spaces to the Herz spaces and are bounded on Morrey-Herz spaces.