Our work is continuation of their work . in this paper , we considered the properties of tg * h functions . the definition of symmetric set in [ 31 is extended to k - th order symmetric set 本文主要在baernstein [ 2 ]及王鍵[ 3 ]關于積分平均值方面所做工作的基礎上,對t _ g ~ * h函數(shù)的性質(zhì)進行研究,作出一些討論。