Bochner-Riesz算子及其高阶交换子L^p有界的必要条件

Necessary Condition Boundedness of Bochner-Riesz Operator and Its Higher Commutators

通过选择适当的Lp函数并应用连续分解方法,给出了低于临界阶的Bochner-Riesz算子在Lp空间有界的新的证明,同时得到了该算子和Lipschitz函数构成的高阶交换子Lp有界性的必要条件.

In terms of continuous decomposition and choosing an appropriate L^p function, the author poses a new method to prove the necessary condition for L^p boundedness of Bochner-Riesz operators below the critical index. And a similar necessary condition for L^p-boundedness of higher order commutators generated by Bochner-Riesz operators below the critical index and Lipschitz functions is obtained by this method.