ANOTHER CHARACTERIZATIONS OF MUCKENHOUPT Ap CLASS

Dinghuai WANG; Jiang ZHOU; Wenyi CHEN

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

Acta mathematica scientia, Series B >

2017 , Vol. 37 >Issue 6: 1761 - 1774

DOI: https://doi.org/10.1016/S0252-9602(17)30105-4

Articles

ANOTHER CHARACTERIZATIONS OF MUCKENHOUPT A_p CLASS

Dinghuai WANG ,
Jiang ZHOU ,
Wenyi CHEN

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

Received date: 2016-07-18

Revised date: 2016-10-24

Online published: 2017-12-25

Supported by

The research was supported by National Natural Science Foundation of China (Grant No.11661075).

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Abstract

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.

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

Cite this article

Dinghuai WANG , Jiang ZHOU , Wenyi CHEN . ANOTHER CHARACTERIZATIONS OF MUCKENHOUPT A_p CLASS[J]. Acta mathematica scientia, Series B, 2017 , 37(6) : 1761 -1774 . DOI: 10.1016/S0252-9602(17)30105-4

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