• Title, Summary, Keyword: Bergman space

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THE BERGMAN METRIC AND RELATED BLOCH SPACES ON THE EXPONENTIALLY WEIGHTED BERGMAN SPACE

  • Byun, Jisoo;Cho, Hong Rae;Lee, Han-Wool
    • East Asian mathematical journal
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    • v.37 no.1
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    • pp.19-32
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    • 2021
  • We estimate the Bergman metric of the exponentially weighted Bergman space and prove many different geometric characterizations for related Bloch spaces. In particular, we prove that the Bergman metric of the exponentially weighted Bergman space is comparable to some Poincaré type metric.

WEIGHTED COMPOSITION OPERATORS FROM BERGMAN SPACES INTO WEIGHTED BLOCH SPACES

  • LI SONGXIAO
    • Communications of the Korean Mathematical Society
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    • v.20 no.1
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    • pp.63-70
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    • 2005
  • In this paper we study bounded and compact weighted composition operator, induced by a fixed analytic function and an analytic self-map of the open unit disk, from Bergman space into weighted Bloch space. As a corollary, obtain the characterization of composition operator from Bergman space into weighted Bloch space.

WEIGHTED HARMONIC BERGMAN FUNCTIONS ON HALF-SPACES

  • Koo, HYUNGWOON;NAM, KYESOOK;YI, HEUNGSU
    • Journal of the Korean Mathematical Society
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    • v.42 no.5
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    • pp.975-1002
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    • 2005
  • On the setting of the upper half-space H of the Eu­clidean n-space, we show the boundedness of weighted Bergman projection for 1 < p < $\infty$ and nonorthogonal projections for 1 $\leq$ p < $\infty$ . Using these results, we show that Bergman norm is equiva­ lent to the normal derivative norms on weighted harmonic Bergman spaces. Finally, we find the dual of b$\_{$^{1}$.

LIPSCHITZ TYPE CHARACTERIZATIONS OF HARMONIC BERGMAN SPACES

  • Nam, Kyesook
    • Bulletin of the Korean Mathematical Society
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    • v.50 no.4
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    • pp.1277-1288
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    • 2013
  • Wulan and Zhu [16] have characterized the weighted Bergman space in the setting of the unit ball of $C^n$ in terms of Lipschitz type conditions in three different metrics. In this paper, we study characterizations of the harmonic Bergman space on the upper half-space in $R^n$. Furthermore, we extend harmonic analogues in the setting of the unit ball to the full range 0 < p < ${\infty}$. In addition, we provide the application of characterizations to showing the boundedness of a mapping defined by a difference quotient of harmonic function.

COMMUTATIVITY AND HYPONORMALITY OF TOEPLITZ OPERATORS ON THE WEIGHTED BERGMAN SPACE

  • Lu, Yufeng;Liu, Chaomei
    • Journal of the Korean Mathematical Society
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    • v.46 no.3
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    • pp.621-642
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    • 2009
  • In this paper we give necessary and sufficient conditions that two Toeplitz operators with monomial symbols acting on the weighted Bergman space commute. We also present necessary and sufficient conditions for the hyponormality of Toeplitz operators with some special symbols on the weighted Bergman space. All the results are stated in terms of the Mellin transform of the symbol.

Poisson integrals contained in harmonic bergman spaces on upper half-space

  • Yi, Heung-Su
    • Communications of the Korean Mathematical Society
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    • v.12 no.1
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    • pp.51-58
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    • 1997
  • On the setting of the upper half-space, H of the euclidean n-space, we consider the question of when the Poisson integral of a function on the boundary of H is a harmonic Bergman function and here we give a partial answer.

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