Communications of the
Korean Mathematical Society CKMS

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

MSC numbers: 45E10, 47B35, 47B20