Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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TOEPLITZ TYPE OPERATOR IN ℂn

  • Choi, Ki Seong (Department of Information Security Konyang University)
  • Received : 2014.09.22
  • Accepted : 2014.10.20
  • Published : 2014.11.15
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Abstract

For a complex measure ${\mu}$ on B and $f{\in}L^2_a(B)$, the Toeplitz operator $T_{\mu}$ on $L^2_a(B,dv)$ with symbol ${\mu}$ is formally defined by $T_{\mu}(f)(w)=\int_{B}f(w)\bar{K(z,w)}d{\mu}(w)$. We will investigate properties of the Toeplitz operator $T_{\mu}$ with symbol ${\mu}$. We define the Toeplitz type operator $T^r_{\psi}$ with symbol ${\psi}$, $$T^r_{\psi}f(z)=c_r\int_{B}\frac{(1-{\parallel}w{\parallel}^2)^r}{(1-{\langle}z,w{\rangle})^{n+r+1}}{\psi}(w)f(w)d{\nu}(w)$$. We will also investigate properties of the Toeplitz type operator with symbol ${\psi}$.

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References

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