On some extension property for $BMO$ functions on Riemann surfaces
On some extension property for $BMO$ functions on Riemann surfaces
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关于黎曼曲面上 $BMO$ 函数的某些扩展性质
DOI：
10.1215/kjm/1250520564
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发表时间：
1988
期刊：
影响因子：
--
通讯作者：
Yasuhiro Gotoh
中科院分区：
文献类型：
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作者：
Yasuhiro Gotoh
In previous papers [6 ] and [7 ] we investigated two BMO spaces BMO(R, in) and B M O(R , A ) on Riemann surface R with universal covering D = z I <11. with respect to Lebesgue measure dm = dxdy on the unit disk D and the hyperbolic measure cl2=-dxdy1(1-1z1 2 ) 2 o n D . These spaces are defined by using the universal covering map. On the other hand, in case Q is a plane domain, we can consider another B M O space BMO(D, m) with respect to Lebesgue measure dm on Q, which seems to be more natural than BM0(f2, in ) . R eim ann [11 ] and Jones [8 ] proved the quasi-conformal invariance of the space BMO(D, m), which shows that this space depends only on the conformal structure of Q. From such an observation we shall define in this paper a new space B M O(R , m ) on an arbitrary Riem ann surface R and investigate its fundamental property.
