关于R^n中实单位球上M—调和BMO函数的Carleson测度特征

ON THE CARLESON MESEASURE CHARACTERIZATION OF M-HARMONIC BMO FUNCTIONSIN THE UNIT BALL OF R^n

本文讨论了实单位球上的平均有界振动M—调和函数的Carleson测度特征,证明了Mobius不变调和函数f(x)属于BMOH或VMOH当且仅当dμ(x)=(1-|x|~2)|f(x)|~2dv(x)是Carleson测度或紧Carleson测度。

This paper discusses the characterization of M-harmonic functions of bounded mean oscillation on the unit ball B in IRn. The authors prove that a Mobius invariant harmonic function f(x) belongs to BMOH or VMOH if and only if du(x) = (1 - |x|2)| f(x)|2dv(x) is a Carleson measure or vanishing Carleson measure.