• 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.

• Honam Mathematical Journal
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• v.43 no.1
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• pp.59-67
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• 2021

We characterize pluriharmonic symbols of the finite rank little Hankel operators on the Dirichlet space of the unit polydisk.

• Journal of the Korean Mathematical Society
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• v.54 no.2
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• pp.627-645
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• 2017

In this paper, we characterize the boundedness, compactness and essential norm of products of differentiation and composition operators from the Bloch space and weighted Dirichlet spaces to analytic Morrey type spaces.

• Honam Mathematical Journal
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• v.39 no.2
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• pp.175-185
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• 2017

In this paper we consider Toeplitz operators on the pluriharmonic Dirichlet space of the unit ball in the n-dimensional complex space. We then characterize Fredholm Toeplitz operators and describe the essential spectrum of a Toeplitz operator as a consequence.

• Bulletin of the Korean Mathematical Society
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• v.57 no.2
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• pp.509-520
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• 2020

We study the Toeplitz operators on the holomorphic and pluriharmonic Dirichlet spaces of the polydisk in terms of when Toeplitz operator is Fredholm operator there. Consequently, we describe the essential spectrum of Toeplitz operators.

• Bulletin of the Korean Mathematical Society
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• v.61 no.4
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• pp.875-895
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• 2024

In this paper, we completely characterize the Schatten classes of composition operators on the Dirichlet type spaces with superharmonic weights. Our investigation is basced on building a bridge between the Schatten classes of composition operators on the weighted Dirichlet type spaces and Toeplitz operators on weighted Bergman spaces.

• Bulletin of the Korean Mathematical Society
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• v.56 no.2
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• pp.319-331
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• 2019

On the weighted Dirichlet space, by the Sobolev's embedding theorem, we characterize the compactness for operators which are finite sums of products of several Toeplitz operators. Moreover, the essential spectrum of Toeplitz operator is characterized.

• Honam Mathematical Journal
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• v.41 no.3
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• pp.619-629
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• 2019

On the setting of the pluriharmonic Dirichlet space, we describe the essential norm of an operator which is a finite sum of products of several Toeplitz operators.

• Communications of the Korean Mathematical Society
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• v.34 no.2
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• pp.533-542
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• 2019

We study commutants of Toeplitz operators acting on the Dirichlet space of the unit disk and prove that an operator in the Toeplitz algebra commuting with a Toeplitz operator with a nonconstant polynomial symbol must be a Toeplitz operator with an analytic symbol.

• Bulletin of the Korean Mathematical Society
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• v.60 no.1
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• pp.161-170
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• 2023

We consider dual Toeplitz operators acting on the orthogonal complement of the Dirichlet space on the unit disk. We give a characterization of when a finite sum of products of two dual Toeplitz operators is equal to 0. Our result extends several known results by using a unified way.