李騰飛

(汕尾職業(yè)技術(shù)學(xué)院信息工程系，汕尾廣東 516600)

Bergman型空間的Littlewood-Paley型定理

李騰飛

(汕尾職業(yè)技術(shù)學(xué)院信息工程系，汕尾廣東 516600)

在Hardy空間上有Littlewood-Paley g-函數(shù)刻畫已被人們熟知，本文證明在Bergman型空間上也有Littlewood-Paley g-函數(shù)刻畫。

Bergman型空間；Hardy空間；Littlewood-Paley g-函數(shù)；原子分解理論

1 引言

對于0

則稱函數(shù)f屬于Hardy空間Hp.?f∈Hp，它的徑向極限幾乎處處存在，記為

(1.1)

和

(1.2)

對所有z∈D∪T.Littlewood和paley[2]證明了

‖f‖Lp(T)≈‖d(f)‖Lp(T).

(1.3)

和

‖f-f(0)‖Lp(T)≈‖(f)‖Lp(T).

(1.4)

符號說明：對于兩個函數(shù)F和G，如果存在常數(shù)c>0，與F和G無關(guān)，使得F

2 主要結(jié)論

(2.1)

定理2.1 設(shè)0

(2.2)

證明 令0

推論2.1 設(shè)0

(2.3)

定理2.2 設(shè)0

(2.4)

證明 記fr(z)=f(rz),0

下面考慮函數(shù)

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[4]Frazier M,Jawerth B,Weiss G.Littlewood-Paley theory and the study of function spaces[C].Providence RI: American Mathematical Society,1991.

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[7]Hedenmalm H,Korenblum B,Zhu K.Theory of Bergman spaces[M].New York:Springer-Verlag,2000.

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

[9]K Avetisyan,S Stevi.Equivalent conditions for Bergman space and Littlewood-Paley type inequalities[J].Journal of Computational Analysis & Applications,2007,9(1):15-28.

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[11]GR Ning，XY Wu，KY Cai.The degree sequence of a Scale-Free random graph process with hard copying[J]. Mathematics,2008:256-269.

[12]M Frazier,B Jawerth,G Weiss.Littlewood-Paley theory and the study of function spaces[C].The conference board of the mathematics,1991,79(7):132.

[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

李騰飛(1976- )，男，講師，碩士，從事數(shù)學(xué)基礎(chǔ)教學(xué)及研究。

O177.91

A

2095-7602(2017)08-0014-04