• 제목/요약/키워드: Dirichlet space

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Multipliers on the dirichlet space $D(Omega)$

  • Nah, Young-Chae
    • 대한수학회논문집
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    • 제10권3호
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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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THE FOCK-DIRICHLET SPACE AND THE FOCK-NEVANLINNA SPACE

  • Cho, Hong Rae;Park, Soohyun
    • East Asian mathematical journal
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    • 제38권5호
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    • pp.643-647
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    • 2022
  • Let F2 denote the space of entire functions f on ℂ that are square integrable with respect to the Gaussian measure $dG(z)={\frac{1}{\pi}}{e^{-{\mid}z{\mid}^2}}$, where dA(z) = dxdy is the ordinary area measure. The Fock-Dirichlet space $F^2_{\mathcal{D}}$ consists of all entire functions f with f' ∈ F2. We estimate Taylor coefficients of functions in the Fock-Dirichlet space. The Fock-Nevanlinna space $F^2_{\mathcal{N}}$ consists of entire functions that possesses just a bit more integrability than square integrability. In this note we prove that $F^2_{\mathcal{D}}=F^2_{\mathcal{N}}$.