• Title, Summary, Keyword: Dirichlet space

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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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COMMUTANTS OF TOEPLITZ OPERATORS WITH POLYNOMIAL SYMBOLS ON THE DIRICHLET SPACE

  • Chen, Yong;Lee, Young Joo
    • 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.

DIRICHLET-JORDAN THEOREM ON $SIM$ SPACE

  • Kim, Hwa-Joon;Lekcharoen, S.;Supratid, S.
    • Korean Journal of Mathematics
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    • v.17 no.1
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    • pp.37-41
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    • 2009
  • We would like to propose Dirichlet-Jordan theorem on the space of summable in measure(SIM). Surely, this is a kind of extension of bounded variation([1, 4]), and considered as an application of fuzzy set such that ${\alpha}$-cut is 0.

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THE CORONA THEOREM FOR BOUNDED FUNCTIONS IN DIRICHLET SPACE

  • Nah, Young-Chae
    • Journal of the Chungcheong Mathematical Society
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    • v.10 no.1
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    • pp.141-146
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    • 1997
  • In this paper we prove that the corona theorem for the algebra $H^{\infty}(D){\cap}D(D)$. That is, we prove that $\mathcal{M}{\setminus}{\overline{D}}$ is an empty set where $\mathcal{M}$ is the maximal ideal space of the given algebra.

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