紧Lie群上Hp（0＜P＜1）函数的临界阶Bochner－Riesz平均算子的有界性

Boundedness of Bochner-Riesz Means Operators at Critical Index of Hp Functions on Compact Lie Groups

中文关键词:  紧Lie群  H（p  ∞）空间  Bochner－Riesz平均算子  H^p空间

英文关键词:compact Lie group  Bochner-Riesz means  H^p space.

中文摘要:

      本文利用尺度‖·‖_H(p,∞)研究了一般紧Ｌｉｅ群上Ｈ^p函数的临界阶Ｂｏｃｈｎｅｒ－Ｒｉｅｓｚ平均算子σ_R^δ:f→σ_R^δf的有界性，得到了如下结果：σ_R^δ是（Ｈ^p，Ｈ（ｐ，∞））型的，并且‖σ_R^δf‖_H(p,∞)≤C‖f‖_H^p

英文摘要:

      In terms of the scale‖·‖_H(p,∞),the boundedness of Bochner-Riesz means operators σ_R^δ:f→σ_R^δf at critical index of H^p functions on compact Lie groups is studied. It is proved that σ_R^δ is of (H^p,H(p,∞))type and ‖σ_R^δf‖_H(p,∞)≤C‖f‖_H^p, where C is inde-pendent of f and R.