数学物理学报(英文版) ›› 2000, Vol. 20 ›› Issue (2): 273-277.

• 论文 • 上一篇    下一篇

WEIGHTED HILBERT TRANSFORM AND Ba METRIC

 丁毅   

  1. Mathematical Department, New Jersey City University, Jersey City, NJ 07305,USA
  • 出版日期:2000-04-18 发布日期:2000-04-18

WEIGHTED HILBERT TRANSFORM AND Ba METRIC

 DING Yi   

  1. Mathematical Department, New Jersey City University, Jersey City, NJ 07305,USA
  • Online:2000-04-18 Published:2000-04-18

摘要:

In the paper, the author generalized the Hardy and Littlewood’s theorem to
Ba space, i.e. for all Pm satisfying 1 < = inf pm ≤ ≤ sup pm < ∞,m = 1, 2, · · · , and
− 1
pm
< s < 1 − 1
pm
, the following inequality
k|x|sHfkBa ≤ A , ,sk|x|sfkBa
holds if and only if −1
< s < 1 − 1
.

关键词: Hilbert transformation, Ba space

Abstract:

In the paper, the author generalized the Hardy and Littlewood’s theorem to
Ba space, i.e. for all Pm satisfying 1 < = inf pm ≤ ≤ sup pm < ∞,m = 1, 2, · · · , and
− 1
pm
< s < 1 − 1
pm
, the following inequality
k|x|sHfkBa ≤ A , ,sk|x|sfkBa
holds if and only if −1
< s < 1 − 1
.

Key words: Hilbert transformation, Ba space

中图分类号: 

  • 45E