| 有非负Ricci曲率的度量测度空间上调和函数的边界问题 |
| |
| 引用本文： | 杨婉婉,李波. 有非负Ricci曲率的度量测度空间上调和函数的边界问题[J]. 数学进展, 2021, 0(2): 245-258 |
| |
| 作者姓名： | 杨婉婉 李波 |
| |
| 作者单位： | 天津大学应用数学中心 |
| |
| 基金项目： | 国家自然科学基金(Nos.11922114,11671039,11771043)。 |
| |
| 摘 要： | 设(X,d,μ)是满足非负Ricci曲率条件的度量测度空间.本文研究了(开)上半空间X×R+上调和函数的边界问题.我们得到了:若u(x,t)是定义在上半空间X×R+上的调和函数,且满足Carleson测度条件supxB,rB∫rB0fB(xB,rB)|t▽u(x,t)|2dμ(x)dt/t≤C＜∞,其中▽=(▽x,?)...
|
| 关 键 词： | 调和函数 度量测度空间 有界平均振动 Carleson测度 |
Boundary Behavior of Harmonic Functions on Metric Measure Spaces with Non-negative Ricci Curvature |
| |
| YANG Wanwan,LI Bo. Boundary Behavior of Harmonic Functions on Metric Measure Spaces with Non-negative Ricci Curvature[J]. Advances in Mathematics(China), 2021, 0(2): 245-258 |
| |
| Authors: | YANG Wanwan LI Bo |
| |
| Affiliation: | (Center for Applied Mathematics,Tianjin University,Tianjin,300072,P.R.China) |
| |
| Abstract: | Let(X,d,μ)be a metric measure space with non-negative Ricci curvature.This paper is concerned with the boundary behavior of harmonic function on the(open)upper halfspace X x R+.We derive that a function f of bounded mean oscillation(BMO)is the trace of harmonic function u(x,t)on X x R+,u(x,0)=f(x),whenever u satisfies the following Carleson measure condition sup xB rB∫rB0fB(xB,xB)|t▽u(x,t)|2dμ(x)dt/t≤C<∞where▽=(▽x,■t)denotes the total gradient and B(xB,rB)denotes the(open)ball centered at xB with radius rB.Conversely,the above condition characterizes all the harmonic functions whose traces are in BMO space. |
| |
| Keywords: | harmonic function metric measure space BMO Carleson measure |
| 本文献已被 维普 等数据库收录！ |
|
