球面分数次积分的Zygmund性质

设Ｓθ是ｎ维单位球面上的平移算子，对于ｐ≥１，Λｐ（α，β）是Ｚｙｇｍｕｎｄ类：Λｐ（α，β）＝｛ｆ（ｘ）Ｓθ（ｆ）－ｆｐ≤ｃｆθα（ｌｏｇ２πθ）β｝，０＜α≤１，β≥０．讨论了球面分数次积分的Ｚｙｇｍｕｎｄ性质．

球面上的分数次积分

设 Ｓ_θ是 ｎ维单位球面 Ω_ｎ上的平移算子， ｐ≥ １，定义平均意义下的Ｌｉｐｓｃｈｉｔｚ空间： ∧_ａ~ｐ＝｛ｆ（ｘ）：｜｜Ｓ_θ（ｆ）－ｆ｜｜_ｐ≤Ｃ_ｆθ~ａ｝，１＜ａ≤１本文研究球面分数次积分在∧_ａ~ｐ中的性质．

Boundedness of the Littlewood-Paley Operator,the Function g(f),on BMO(T)

Littlewood-Paley operator,the function g(f), is considered as an operator on BMO(T). It is proved that if f E BMO (T), then g(f)∈BMO (T) and there is a constant C that is independent of f such that ‖g(f)‖_* ≤C‖f‖_*. Moreover,we have got the further results.