摘要
该文研究了联系抛物Bessel算子L=∂t-Δx-1/4-μ2 x 2(μ>-1)的Poisson半群的振荡算子.利用抛物半群方法和抛物向量值Calderón-Zygmund理论,证明了振荡算子O(P Lτ)从L p(ℝ2)(1<p<∞)到自身是有界的,从L 1(ℝ2)到弱-L 1(ℝ2)是有界的,而且从L∞c(ℝ2)到BMO(ℝ2)也是有界的.在p=∞的情况下,证明了在某种意义下振荡算子O(P Lτ)的像严格小于标准的奇异积分算子的像.
In this paper,the oscillation of the Poisson semigroup associated with parabolic Bessel operator L=∂t-Δx-1/4-μ2 x 2(μ>-1)is considered.The oscillation operator O(P Lτ)is bounded from L p(ℝ2)(1<p<∞)into itself,from L 1(ℝ2)into weak-L 1(ℝ2),and bounded from L∞c(ℝ2)into BMO(ℝ2)is proved by the parabolic semigroup method and Calderón-Zygmund theory.In the case p=∞,it is showed that the range of the image of the oscillation O(P Lτ)is strictly smaller than the range of a general singular operator in some sense.
作者
马毅
陈淼
陈岩
李平
MA Yi;CHEN Miao;CHEN Yan;LI Ping(School of Information and Mathematics,Yangtze University,Jingzhou 434023,Huibei,China)
出处
《华中师范大学学报（自然科学版）》
CAS
CSCD
北大核心
2023年第3期335-340,共6页
Journal of Central China Normal University：Natural Sciences
基金
国家自然科学基金项目(12171182)。
作者简介
通信联系人:李平.E-mail:chenyanai_0720@163.com.
