Boundary behavior of harmonic functions on metric measure spaces with non-negative Ricci curvature  

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作  者:Wanwan YANG Bo LI 

机构地区:[1]Center for Applied Mathematics,Tianjin University,Tianjin 300072,China

出  处:《Frontiers of Mathematics in China》2022年第3期455-471,共17页中国高等学校学术文摘·数学(英文)

摘  要: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 half-space X×R_(+).We derive that a function f of bounded mean oscillation(BMO)is the trace of harmonic function u(x,t)on X×R_(+),u(x,0)=f(x),whenever u satisfies the following Carleson measure condition supx_(B),r_(B) ∫_(0)^(r_(B) ) f_(B(x_(B),r_(B))) |t■u(x,t)|^(2)dμ(x)dt/t≤C<∞,where ■=(■_(x),■_(t))denotes the total gradient and B(x_(B),r_(B)) denotes the(open)ball centered at x_(B) with radius r_(B).Conversely,the above condition characterizes all the harmonic functions whose traces are in BMO space.

关 键 词:Harmonic function metric measure space BMO Carleson measure 

分 类 号:O17[理学—数学]

 

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