• Title/Summary/Keyword: Bergman spaces

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TOEPLITZ OPERATORS ON BLOCH-TYPE SPACES AND A GENERALIZATION OF BLOCH-TYPE SPACES

  • Kang, Si Ho
    • Journal of the Chungcheong Mathematical Society
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    • v.27 no.3
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    • pp.439-454
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    • 2014
  • We deal with the boundedness of the n-th derivatives of Bloch-type functions and Toeplitz operators and give a relationship between Bloch-type spaces and ranges of Toeplitz operators. Also we prove that the vanishing property of ${\parallel}uk^{\alpha}_z{\parallel}_{s,{\alpha}}$ on the boundary of $\mathbb{D}$ implies the compactness of Toeplitz operators and introduce a generalization of Bloch-type spaces.

Multipliers on the dirichlet space $D(Omega)$

  • Nah, Young-Chae
    • Communications of the Korean Mathematical Society
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    • v.10 no.3
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    • pp.633-642
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    • 1995
  • Recently S. Axler proved that every sequence in the unit disk U converging to the boundary contains an interpolating subsequence for the multipliers of the Dirichlet space D(U). In this paper we generalizes Axler's result to the finitely connected planer domains such that the Dirichlet spaces are contained in the Bergman spaces.

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REDUCING SUBSPACES FOR A CLASS OF TOEPLITZ OPERATORS ON WEIGHTED HARDY SPACES OVER BIDISK

  • Kuwahara, Shuhei
    • Bulletin of the Korean Mathematical Society
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    • v.54 no.4
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    • pp.1221-1228
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    • 2017
  • We consider weighted Hardy spaces on bidisk ${\mathbb{D}}^2$ which generalize the weighted Bergman spaces $A^2_{\alpha}({\mathbb{D}}^2)$. Let z, w be coordinate functions and $T_{{\bar{z}}^N}_w$ Toeplitz operator with symbol $_{{\bar{z}}^N}_w$. In this paper, we study the reducing subspaces of $T_{{\bar{z}}^N}_w$ on the weighted Hardy spaces.

MULTIPLIERS OF WEIGHTED BLOCH SPACES AND BESOV SPACES

  • Yang, Gye Tak;Choi, Ki Seong
    • Journal of the Chungcheong Mathematical Society
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    • v.22 no.4
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    • pp.727-737
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    • 2009
  • Let M(X) be the space of all pointwise multipliers of Banach space X. We will show that, for each $\alpha>1$, $M(\mathfrak{B}_\alpha)=M(\mathfrak{B}_{\alpha,0})=H^\infty{(B)}$. We will also show that, for each $0<{\alpha}<1$, $M(\mathfrak{B}_\alpha)$ and $M(\mathfrak{B}_{\alpha,0})$ are Banach algebras. It is established that certain inclusion relationships exist between the weighted Bloch spaces and holomorphic Besov spaces.

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THE TOEPLITZ OPERATOR INDUCED BY AN R-LATTICE

  • Kang, Si Ho
    • Journal of the Chungcheong Mathematical Society
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    • v.25 no.3
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    • pp.491-499
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    • 2012
  • The hyperbolic metric is invariant under the action of M$\ddot{o}$bius maps and unbounded. For 0 < $r$ < 1, there is an r-lattice in the Bergman metric. Using this r-lattice, we get the measure ${\mu}_r$ and the Toeplitz operator $T^{\alpha}_{\mu}_r$ and we prove that $T^{\alpha}_{\mu}_r$ is bounded and $T^{\alpha}_{\mu}_r$ is compact under some condition.

THE ATOMIC DECOMPOSITION OF HARMONIC BERGMAN FUNCTIONS, DUALITIES AND TOEPLITZ OPERATORS

  • Lee, Young-Joo
    • Bulletin of the Korean Mathematical Society
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    • v.46 no.2
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    • pp.263-279
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    • 2009
  • On the setting of the unit ball of ${\mathbb{R}}^n$, we consider a Banach space of harmonic functions motivated by the atomic decomposition in the sense of Coifman and Rochberg [5]. First we identify its dual (resp. predual) space with certain harmonic function space of (resp. vanishing) logarithmic growth. Then we describe these spaces in terms of boundedness and compactness of certain Toeplitz operators.

WEIGHTED COMPOSITION OPERATORS WHOSE RANGES CONTAIN THE DISK ALGEBRA II

  • Izuchi, Kei Ji;Izuchi, Kou Hei;Izuchi, Yuko
    • Bulletin of the Korean Mathematical Society
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    • v.55 no.2
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    • pp.507-514
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    • 2018
  • Let $\{{\varphi}_n\}_{n{\geq}1}$ be a sequence of analytic self-maps of ${\mathbb{D}}$. It is proved that if the union set of the ranges of the composition operators $C_{{\varphi}_n}$ on the weighted Bergman spaces contains the disk algebra, then ${\varphi}_k$ is an automorphism of ${\mathbb{D}}$ for some $k{\geq}1$.