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HYPONORMAL SINGULAR INTEGRAL OPERATORS WITH CAUCHY KERNEL ON L2

  • Nakazi, Takahiko (Hokkaido University)
  • Received : 2017.04.07
  • Accepted : 2017.12.29
  • Published : 2018.07.31

Abstract

For $1{\leq}p{\leq}{\infty}$, let $H^p$ be the usual Hardy space on the unit circle. When ${\alpha}$ and ${\beta}$ are bounded functions, a singular integral operator $S_{{\alpha},{\beta}}$ is defined as the following: $S_{{\alpha},{\beta}}(f+{\bar{g}})={\alpha}f+{\beta}{\bar{g}}(f{\in}H^p,\;g{\in}zH^p)$. When p = 2, we study the hyponormality of $S_{{\alpha},{\beta}}$ when ${\alpha}$ and ${\beta}$ are some special functions.

Keywords

singular integral operator;Toeplitz operator;Hardy space;hyponormal operator

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