Bergman型空间的Littlewood-Paley型定理

李腾飞

(汕尾职业技术学院信息工程系，汕尾广东 516600)

Bergman型空间的Littlewood-Paley型定理

李腾飞

(汕尾职业技术学院信息工程系，汕尾广东 516600)

在Hardy空间上有Littlewood-Paley g-函数刻画已被人们熟知，本文证明在Bergman型空间上也有Littlewood-Paley g-函数刻画。

Bergman型空间；Hardy空间；Littlewood-Paley g-函数；原子分解理论

1 引言

对于0

则称函数f属于Hardy空间Hp.∀f∈Hp，它的径向极限几乎处处存在，记为

(1.1)

和

(1.2)

对所有z∈D∪T.Littlewood和paley[2]证明了

‖f‖Lp(T)≈‖d(f)‖Lp(T).

(1.3)

和

‖f-f(0)‖Lp(T)≈‖(f)‖Lp(T).

(1.4)

符号说明：对于两个函数F和G，如果存在常数c>0，与F和G无关，使得F

2 主要结论

(2.1)

定理2.1 设0

(2.2)

证明 令0

推论2.1 设0

(2.3)

定理2.2 设0

(2.4)

证明 记fr(z)=f(rz),0

下面考虑函数

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[8]Stein E M.Topics in Harmonic Analysis Related to the Littlewood-Paley Theory[M].Princeton,New Jersey: Princeton University Press,1970.

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[13]Zeqian Chen,Wei Ouyang.Tent spaces and Littlewood-Paley g-functions associated with Bergman spaces in the unit ball of C[J].Mathematics,2011,281(3):1-23.

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A Littlewood-Paley Type Theorem for Bergman Type Spaces

LI Teng-fei

(Shanwei Vocational Technical College, Shanwei Guangdong 516600, China)

We are familiar with the Littlewood-Paley -functions characterization of the Hardy space. In this paper, we prove that the original Littlewood-Paley g-functions can be used to characterize Bergman type spaces as well.

Bergman type space; Hardy space; Littlewood-Paley g-function; atomic decomposition

2017-03-13

李腾飞(1976- )，男，讲师，硕士，从事数学基础教学及研究。

O177.91

A

2095-7602(2017)08-0014-04