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smf2828

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[求助] BMO与VMO

请问BMO与VMO这两个函数空间有什么样的关系??
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xxdyt

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【答案】应助回帖

BMO is the space of bounded mean oscillation, that is

\sup_{B}\frac1{B}  \int_B|u-u_B|<\infty

where u_B=\frac1{B}\int_B u.

VMO is the closure of compact support functions in BMO space.

But there are also some other kinds of VMO. So you should be careful.
2楼2013-05-30 11:19:16
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xxdyt

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引用回帖:
2楼: Originally posted by xxdyt at 2013-05-30 11:19:16
BMO is the space of bounded mean oscillation, that is

\sup_{B}\frac1{B}  \int_B|u-u_B|<\infty

where u_B=\frac1{B}\int_B u.

VMO is the closure of compact support functions in BMO space.
...

VMO is the closure of compact support continuous functions in BMO space.
3楼2013-05-30 11:20:21
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4楼2013-07-27 22:55:21
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