姜伟伟, 赵凯. 一类与高阶Schrödinger型算子相关的变分算子的BMO交换子有界性[J]. 云南大学学报(自然科学版), 2021, 43(3): 429-436. doi: 10.7540/j.ynu.20200685
引用本文: 姜伟伟, 赵凯. 一类与高阶Schrödinger型算子相关的变分算子的BMO交换子有界性[J]. 云南大学学报(自然科学版), 2021, 43(3): 429-436. doi: 10.7540/j.ynu.20200685
JIANG Wei-wei, ZHAO Kai. Boundedness of the BMO commutators of the variation operators associated with the high order Schrödinger type operators[J]. Journal of Yunnan University: Natural Sciences Edition, 2021, 43(3): 429-436. DOI: 10.7540/j.ynu.20200685
Citation: JIANG Wei-wei, ZHAO Kai. Boundedness of the BMO commutators of the variation operators associated with the high order Schrödinger type operators[J]. Journal of Yunnan University: Natural Sciences Edition, 2021, 43(3): 429-436. DOI: 10.7540/j.ynu.20200685

一类与高阶Schrödinger型算子相关的变分算子的BMO交换子有界性

Boundedness of the BMO commutators of the variation operators associated with the high order Schrödinger type operators

  • 摘要:\cal L = ( - \Delta )^2 + V^2\bfR^n(n \geqslant 5) 上的高阶Schrödinger型算子,其中非负位势 V 属于反向Hölder类 RH_q\;\bigg(q > \dfracn2\bigg). 记 \cal V_\rho (\rme^ - t\cal L) 为与高阶Schrödinger型算子 \cal L 相关的变分算子. 基于Herz型Hardy空间的原子分解理论,利用Schrödinger型算子的性质,证明了这类变分算子与BMO函数构成的交换子是从Herz-Hardy空间到Herz空间有界的,也是在Morrey-Herz空间上有界的结果.

     

    Abstract: Let \cal L = ( - \Delta )^2 + V^2 be a high order Schrödinger type operator in \rmR^n\;(n \geqslant 5), where V is a nonnegative potential satisfying the reverse Hölder inequality, and \cal V_\rho (\rme^ - t\cal L) be the variation operator associated with the high order Schrödinger type operator. Based on the theory of atomic decompesitions of Herz-Hardy spaces, using the properties of the Schrödinger type operators, the boundedness of the commutators composed by the variation operators associated with the Schrödinger type operators and BMO fuctions from Herz type Hardy spaces into the Herz spaces and the boundedness of the commutators on Morrey-Herz spaces are proved.

     

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