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研究生: 謝旻軒
Hsieh, Min-Hsuan
論文名稱: Some Remarks On Korenblum Conjecture
柯倫步猜想的一些探討
指導教授: 程守慶
Chen, So-Chin
口試委員:
學位類別: 碩士
Master
系所名稱: 理學院 - 數學系
Department of Mathematics
論文出版年: 2010
畢業學年度: 98
語文別: 英文
論文頁數: 19
中文關鍵詞: 柯倫步猜想
外文關鍵詞: Korenblum Conjecture
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  • In this article, we are interested in the theorem which proved by Korenblum, O'neil, Richards, and Zhu. They prove the Korenblum conjecture when either f or g is a monomial.
    So we discuss some special cases from above.


    1 Introduction 1 2 Preliminaries 5 3 Main Results 7

    [1] B. Korenblum, A maximum prinple for the Bergman space, Publ. Math.35(1991), 479-486.
    [2] W. K. Hayman, On a conjecture of Korenblum, Analysis 19(1999),195-205.
    [3] A. Hinkkanen, On a maximum prinple in the Bergman space, Mathe-matique 79(1999), 335-344.
    [4] B. Korenblum, R. O'neil, K. Richards, and K. Zhu, Totally monotonefunctions with applications to the Bergman space, Trans. Amer. Math.Soc. 337(1993), 795-806.
    [5] B. Korenblum, Transformation of zero sets by contractive operators in the Bergmanspace, Bulletin des Sciences Mathematiques, 2e serie,114(1990), 395-394.
    [6] A. Schuster, The maximum principle for the Bergman space and the mÄobius pseudodistance for the annulus, Proc. Amer. Math.Soc.134(2006), 3525-3530.
    [7] C.Wang, Re‾ning the constant in a maximum principle for the Bergman space, Proc. Amer. Math. Soc. 132(2004), 853-855.
    [8] C. Wang, An upper bound on Korenblums constant, Integr. Equ. Oper.Theory, 49(2004), 561-563.
    [9] C. Wang, On Korenblum's constant, J. Math. Anal. Appl. 296(2004),262-264.
    [10] C. Wang, On Korenblum maximum principle, Proc. Amer. Math. Soc.134(2006), 2061-2066.
    [11] C. Shen, A slight improvement to Korenblum's constant, J. Math. Anal.Appl. 337(2008), 464-465.
    [12] C. Wang, Behavior of the constant in Korenblum's maximum principle,Math. Nachr. 281(2008), 447-454
    [13] C. Wang, Domination in the Bergman space and Korenblum's constant,Integr. Equ. Oper. Theory, 61(2008), 423-432.
    [14] S. N. Bernstein, Sur les fonctions absolument monotones, Acta Math.52(1929), 1-66.
    [15] W. Rudin, Real and complex analysis, McGraw-Hill, New York(1987).
    [16] R. Narasimhan, Complex analysis in one variable, University of Chicago,(1971).

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