논문KCI 등재
Weighted composition operators whose ranges contain the disk algebra II
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초록
Let $\{\p_n\}_{n\ge1}$ be a sequence of analytic self-maps of $\D$. It is proved that if the union set of the ranges of the composition operators $C_{\p_n}$ on the weighted Bergman spaces contains the disk algebra, then $\p_k$ is an automorphism of $\D$ for some $k\ge1$.
Abstract
Let $\{\p_n\}_{n\ge1}$ be a sequence of analytic self-maps of $\D$. It is proved that if the union set of the ranges of the composition operators $C_{\p_n}$ on the weighted Bergman spaces contains the disk algebra, then $\p_k$ is an automorphism of $\D$ for some $k\ge1$.
참고문헌 (10)
- C. Cowen, "Composition Operators on Spaces of Analytic Functions" (1995), CRC Press
- J. Garnett, "Bounded Analytic Functions" (1981), Academic Press
- H. Hedenmalm, "Theory of Bergman Spaces" (2000), Springer
- K. Hoffman, "Banach Spaces of Analytic Functions" (1962), Prentice Hall
- K. J. Izuchi, "Weighted composition operators whose ranges contain the disk algebra", Complex Var. Elliptic Equ., 60(7), pp.938~944 (2015)[DOI]
- D. Sarason, "Algebras of functions on the unit circle", Bull. Amer. Math. Soc., 79, pp.286~299 (1973)[DOI]
- D. Sarason, "Functions of vanishing mean oscillation", Trans. Amer. Math. Soc., 207, pp.391~405 (1975)[DOI]
- J. Shapiro, "Composition Operators and Classical Function Theory" (1993), Springer-Verlag
- C. Sundberg, "Interpolating sequences for <TEX>$QA_B$<", TEX>, 1983, pp.276(2), 551~581
- T. Wolff, "Two algebras of bounded functions", Duke Math. J., 49(2), pp.321~328 (1982)[DOI]
관련 논문AI추천
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