ANOTHER CHARACTERIZATIONS OF MUCKENHOUPT Ap CLASS

doi:10.1016/S0252-9602(17)30105-4

数学物理学报(英文版) ›› 2017, Vol. 37 ›› Issue (6): 1761-1774.doi: 10.1016/S0252-9602(17)30105-4

ANOTHER CHARACTERIZATIONS OF MUCKENHOUPT A_p CLASS

王定怀¹, 周疆¹, 陈文艺²

1. College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China;
2. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

收稿日期:2016-07-18 修回日期:2016-10-24 出版日期:2017-12-25 发布日期:2017-12-25
通讯作者: Jiang ZHOU E-mail:Wangdh1990@126.com
作者简介:Dinghuai WANG,zhoujiangshuxue@126.com;Wenyi CHEN,wychencn@hotmail.com
基金资助:
The research was supported by National Natural Science Foundation of China (Grant No.11661075).

ANOTHER CHARACTERIZATIONS OF MUCKENHOUPT A_p CLASS

Dinghuai WANG¹, Jiang ZHOU¹, Wenyi CHEN²

1. College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China;
2. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

Received:2016-07-18 Revised:2016-10-24 Online:2017-12-25 Published:2017-12-25
Contact: Jiang ZHOU E-mail:Wangdh1990@126.com
Supported by:
The research was supported by National Natural Science Foundation of China (Grant No.11661075).

摘要/Abstract

摘要：

This manuscript addresses Muckenhoupt A_p weight theory in connection to Morrey and BMO spaces. It is proved that ω belongs to Muckenhoupt A_p class, if and only if Hardy-Littlewood maximal function M is bounded from weighted Lebesgue spaces L^p(ω) to weighted Morrey spaces M_q^p(ω) for 1 < q < p < ∞. As a corollary, if M is (weak) bounded on M_q^p (ω), then ω ∈ A_p. The A_p condition also characterizes the boundedness of the Riesz transform R_j and convolution operators T_∈ on weighted Morrey spaces. Finally, we show that ω ∈ A_p if and only if ω ∈ BMO^p'(ω) for 1 ≤ p < ∞ and 1/p + 1/p'=1.

关键词: characterization, Hardy-Littlewood maximal function, Muckenhoupt A_p class, weighted Morrey spaces, weighted BMO space

Abstract:

Key words: characterization, Hardy-Littlewood maximal function, Muckenhoupt A_p class, weighted Morrey spaces, weighted BMO space

王定怀, 周疆, 陈文艺. ANOTHER CHARACTERIZATIONS OF MUCKENHOUPT A_p CLASS[J]. 数学物理学报(英文版), 2017, 37(6): 1761-1774.

Dinghuai WANG, Jiang ZHOU, Wenyi CHEN. ANOTHER CHARACTERIZATIONS OF MUCKENHOUPT A_p CLASS[J]. Acta mathematica scientia,Series B, 2017, 37(6): 1761-1774.

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ANOTHER CHARACTERIZATIONS OF MUCKENHOUPT A_p CLASS

ANOTHER CHARACTERIZATIONS OF MUCKENHOUPT A_p CLASS

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