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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.
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참고문헌 (14)
참고문헌 신청
M. B. Abrahamse / 1976 / Subnormal Toeplitz operators and functions of bounded type / Duke Math. J. 43(3):597~604
A. Brown / 1963 / Algebraic properties of Toeplitz operators / J. Reine Angew. Math. 213:89~102
C. C. Cowen / 1988 / Hyponormality of Toeplitz operators / Proc. Amer. Math. Soc. 103(3):809~812
R. G. Douglas / 1966 / On majorization, factorization, and range inclusion of operators on Hilbert space / Proc. Amer. Math. Soc. 17:413~415
I. Gohberg / 1992 / One-dimensional linear singular integral equations. Vol. II, translated from the 1979 German translation by S. Roch and revised by the authors / Operator Theory: Advances and Applications 54
A. Brown / 1963 / Algebraic properties of Toeplitz operators / J. Reine Angew. Math. 213:89~102
C. C. Cowen / 1988 / Hyponormality of Toeplitz operators / Proc. Amer. Math. Soc. 103(3):809~812
R. G. Douglas / 1966 / On majorization, factorization, and range inclusion of operators on Hilbert space / Proc. Amer. Math. Soc. 17:413~415
I. Gohberg / 1992 / One-dimensional linear singular integral equations. Vol. II, translated from the 1979 German translation by S. Roch and revised by the authors / Operator Theory: Advances and Applications 54
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