CRITERIA FOR AN ANALYTIC FUNCTION BELONGING TO QK SPACES

doi:10.1016/S0252-9602(09)60004-7

Acta mathematica scientia,Series B

• Articles • Previous Articles Next Articles

CRITERIA FOR AN ANALYTIC FUNCTION BELONGING TO Q_K SPACES

Hasi Wulan

Department of Mathematics, Shantou University, Shantou 515063, China

Received:2006-10-08 Revised:1900-01-01 Online:2009-02-20 Published:2009-02-20
Contact: Hasi Wulan

Abstract

Abstract:

The author gives a mild integral condition in a nondecreasing function K: [0, ∞) → [0, ∞), which is sufficient and the best possible to ensure that f is a Bloch function if and only if f belongs to Q_K, a Möbius-invariant space of functions
analytic in the unit disk. Their contributions are slight improvements of known results, and the proofs presented here are independently developed. The corresponding results for meromorphic case are also given.

Key words: Areally mean q-valent, circumferentially mean q-valent, Q_K spaces

CLC Number:

30D45

Hasi Wulan. CRITERIA FOR AN ANALYTIC FUNCTION BELONGING TO Q_K SPACES[J].Acta mathematica scientia,Series B, 2009, 29(1): 33-44.

Trendmd

[1]	Daochun SUN, Yingying HUO, Fujie CHAI. NORMAL CRITERIA FOR A FAMILY OF HOLOMORPHIC CURVES [J]. Acta mathematica scientia,Series B, 2021, 41(6): 1887-1895.
[2]	Yuxia LIANG. THE PRODUCT OPERATOR BETWEEN BLOCH-TYPE SPACES OF SLICE REGULAR FUNCTIONS [J]. Acta mathematica scientia,Series B, 2021, 41(5): 1606-1618.
[3]	Pablo GALINDO, Mikael LINDSTRÖM. THE BLOCH SPACE ON THE UNIT BALL OF A HILBERT SPACE: MAXIMALITY AND MULTIPLIERS [J]. Acta mathematica scientia,Series B, 2021, 41(3): 899-906.
[4]	Yong-Kui CHANG, Yanyan WEI. S-ASYMPTOTICALLY BLOCH TYPE PERIODIC SOLUTIONS TO SOME SEMI-LINEAR EVOLUTION EQUATIONS IN BANACH SPACES [J]. Acta mathematica scientia,Series B, 2021, 41(2): 413-425.
[5]	Bingmao DENG, Mingliang FANG, Yuefei WANG. PERIODIC POINTS AND NORMALITY CONCERNING MEROMORPHIC FUNCTIONS WITH MULTIPLICITY [J]. Acta mathematica scientia,Series B, 2020, 40(5): 1429-1444.
[6]	Wei CHEN, Honggen TIAN, Peichu HU. NORMAL FAMILIES OF MEROMORPHIC FUNCTIONS WITH SHARED VALUES [J]. Acta mathematica scientia,Series B, 2016, 36(1): 87-93.
[7]	LI Ye Zhou, QI Jian Ming, YUAN Wen Jun. GROWTH OF MEROMORPHIC SOLUTIONS OF SOME ALGEBRAIC DIFFERENTIAL EQUATIONS [J]. Acta mathematica scientia,Series B, 2015, 35(1): 105-111.
[8]	CAI FuJie GAO Zong Sheng. THE NORMALITY OF ALGEBROID MULTIFUNCTIONS AND THEIR COEFFICIENT FUNCTIONS [J]. Acta mathematica scientia,Series B, 2015, 35(1): 121-132.
[9]	LEI Chun-Lin, FANG Ming-Liang, ZENG Cui-Ping. SOME NORMALITY CRITERIA OF MEROMORPHIC FUNCTIONS [J]. Acta mathematica scientia,Series B, 2013, 33(6): 1667-1674.
[10]	JIANG Yun-Bo, GAO Zong-Sheng. NORMAL FAMILIES OF MEROMORPHIC FUNCTIONS SHARING A HOLOMORPHIC FUNCTION AND THE CONVERSE OF THE BLOCH PRINCIPLE [J]. Acta mathematica scientia,Series B, 2012, 32(4): 1503-1512.
[11]	LI Sheng, GAO Zong-Sheng. RESULTS ON A QUESTION OF ZHANG AND YANG [J]. Acta mathematica scientia,Series B, 2012, 32(2): 717-723.
[12]	DAI Ji-Neng, OUYANG Cai-Heng. COMPACT COMPOSITION OPERATORS ON GENERALIZED LIPSCHITZ SPACES [J]. Acta mathematica scientia,Series B, 2011, 31(4): 1347-1356.
[13]	SUN Dao-Chun, GAO Zong-Sheng. ON THE OPERATIONS OF ALGEBROID FUNCTIONS [J]. Acta mathematica scientia,Series B, 2010, 30(1): 247-256.
[14]	WANG Xiong-Liang, LIU Ta-Shun. COMPOSITION TYPE OPERATORS FROM HARDY SPACES TO μ-BLOCH SPACES ON THE UNIT BALL [J]. Acta mathematica scientia,Series B, 2009, 29(5): 1430-1438.
[15]	TUN Shu-Hong, WANG Mao-Fa, LIU Pei-De. TWO PROBLEMS ABOUT COMPOSITION OPERATORS ON HARDY SPACE [J]. Acta mathematica scientia,Series B, 2005, 25(3): 515-524.

CRITERIA FOR AN ANALYTIC FUNCTION BELONGING TO Q_K SPACES

PDF (PC)

Abstract

Cite this article

share this article

References

Related Articles 15

Metrics

Comments

Recommended 0