圆盘上的BMO_p（D）空间与Bloch空间

BMO_p(D)spaces and Bloch space on the open unit disk in C

在单位圆盘Ｄ上引入了一类函数空间ＢＭＯｐ（Ｄ）和ＶＭＯｐ（Ｄ）（１≤ｐ＜＋∞），讨论了它们与ＺｈｕＫｅｈｅ引入并讨论的函数空间ＢＭＯａ（Ｄ）和ＶＭＯａ（Ｄ）之间的关系；证明了全纯的ＢＭＯｐ（Ｄ）函数为Ｂｌｏｃｈ．函数，全纯的ＶＭＯｐ（Ｄ）函数为小Ｂｌｏｃｈ函数．即ＢＭＯｐ（Ｄ）Ｈ（Ｄ）＝，ＶＭＯｐ（Ｄ）Ｈ（Ｄ）＝。

A family of function spaces BMO.(D) and VMO,(D)(1≤p<+∞) on the open unit disk in C are defined. Relation of these function spaces and the BMO(D), VMO(D)that are defined by Zhu Kehe are discussed. It is proved that holomorphic BMO(D) functions are Bloch functions and holomorphic VMOp(D) functions are little Bloch functions.