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http://dx.doi.org/10.4134/CKMS.c170144

HYPONORMAL SINGULAR INTEGRAL OPERATORS WITH CAUCHY KERNEL ON L2  

Nakazi, Takahiko (Hokkaido University)
Publication Information
Communications of the Korean Mathematical Society / v.33, no.3, 2018 , pp. 787-798 More about this Journal
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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