• Bulletin of the Korean Mathematical Society
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• v.44 no.2
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• pp.281-290
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• 2007

We deal with Bergman functions defined on the half-plane. We study integral operators, and some relationship between Berezin transforms and Toeplitz operators, and also show that some Berezin transforms are Mobius invariant.

• Honam Mathematical Journal
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• v.30 no.1
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• pp.147-164
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• 2008

In the setting of the half-plane of the complex plane, we show that for r > $-{\frac{1}{2}}$, the dual space of the weighted Bergman spaces $B^{1,r}$ is the Bloch space and we introduce some operators. We also study Toeplitz and Hankel operators and we find some characterization of Hankel operators.

• Honam Mathematical Journal
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• v.35 no.3
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• pp.343-350
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• 2013

In this paper we prove that if Toeplitz operators $T^{\alpha}_u$ with symbols in RW satisfy ${\parallel}uk^{\alpha}_z{\parallel}_{s,{\alpha}{\rightarrow}0$ as $z{\rightarrow}{\partial}\mathbb{D}$ then $T^{\alpha}_u$ is compact and also prove that if $T^{\alpha}_u$ is compact then the Berezin transform of $T^{\alpha}_u$ equals to zero on ${\partial}\mathbb{D}$.

• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.507-513
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• 2018

We will consider the asymptotic toeplitzness associated with weighted composition operators on the Hardy-Hilbert space $H^2$.

• 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.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.3
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• pp.471-479
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• 2010

For a complex regular Borel measure ${\mu}$ on ${\Omega}$ which is a subset of ${\mathbb{C}}^k$, where k is a positive integer we define the Toeplitz operator $T_{\mu}$ on a reproducing analytic space which comtains polynomials. Using every symmetric polynomial is a polynomial of elementary polynomials, we show that if $T_{\mu}$ has finite rank then ${\mu}$ is a finite linear combination of point masses.

• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1471-1481
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• 2016

We characterize reducing subspaces of weighted shifts with operator weights as wandering invariant subspaces of the shifts with additional structures. We show how some earlier results on reducing subspaces of powers of weighted shifts with scalar weights on the unit disk and the polydisk can be fitted into our general framework.

• 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.

• 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.