• 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.

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.

NORM AND ESSENTIAL NORM ESTIMATES OF TOEPLITZ OPERATORS ON THE BERGMAN SPACE

  • Choe, Boo-Rim;Lee, Young-Joo
    • Communications of the Korean Mathematical Society
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    • v.11 no.4
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    • pp.937-958
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    • 1996
  • On the setting of product of balls we consider Toeplitz operators, with symbols satisfying a certain condition, on the Bergman space. Norms and essential norms of such operators are estimated by means of certain integral quantities.

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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.

HYPONORMAL TOEPLITZ OPERATORS ON THE BERGMAN SPACE. II.

  • Hwang, In-Sung;Lee, Jong-Rak
    • Bulletin of the Korean Mathematical Society
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    • v.44 no.3
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    • pp.517-522
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    • 2007
  • In this paper we consider the hyponormality of Toeplitz operators $T_\varphi$ on the Bergman space $L_\alpha^2(\mathbb{D})$ with symbol in the case of function $f+\bar{g}$ with polynomials f and g. We present some necessary conditions for the hyponormality of $T_\varphi$ under certain assumptions about the coefficients of $\varphi$.

HYPONORMALITY OF TOEPLITZ OPERATORS ON THE BERGMAN SPACE

  • Hwang, In-Sung
    • Journal of the Korean Mathematical Society
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    • v.45 no.4
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    • pp.1027-1041
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    • 2008
  • In this paper we consider the hyponormality of Toeplitz operators $T_{\varphi}$ on the Bergman space $L_a^2{(\mathbb{D})$ in the cases, where ${\varphi}\;:=f+\bar{g}$ (f and g are polynomials). We present some necessary or sufficient conditions for the hyponormality of $T_{\varphi}$ under certain assumptions about the coefficients of ${\varphi}$.

REDUCING SUBSPACES FOR TOEPLITZ OPERATORS ON THE POLYDISK

  • Shi, Yanyue;Lu, Yufeng
    • Bulletin of the Korean Mathematical Society
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    • v.50 no.2
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    • pp.687-696
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    • 2013
  • In this note, we completely characterize the reducing subspaces of $T_{{z^N_1}{z^M_2}}$ on $A^2_{\alpha}(D^2)$ where ${\alpha}$ > -1 and N, M are positive integers with $N{\neq}M$, and show that the minimal reducing subspaces of $T_{{z^N_1}{z^M_2}}$ on the unweighted Bergman space and on the weighted Bergman space are different.