广义Bochner-Riesz乘子的等价性及其应用——献给陆善镇教授75华诞

本文研究下面这两个函数,（1-｜x｜^ρ1）＋^α和（1-｜x｜^ρ2）＋^α,其中ρ1,ρ2和α均为正实数,文献上称这类函数为广义Bochner-Riesz乘子.本文将证明,当α给定时,对任意的ρ1〉0和ρ2〉0,这两个函数作为乘子,其乘子算子的L^p有界性和Hp有界性是等价的.

The equivalence of a class of generalized Bochner-Riesz multipliers and its applications

We consider the following two functions, (1-|x|^ρ1)₊^α and (1-|x|^ρ2)₊^α + which are called the generalized Bochner-Riesz multipliers, where ρ1, ρ2 and α are positive real numbers. We shall prove that, as the multiplier operators with respect to the two functions, their L^p-boundedness and H^p-boundedness are equivalent for any ρ1, ρ2 and α.