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Let $\mbox{HE}_I$, $\mbox{HE}_{II}$, $\mbox{HE}_{III}$ and $\mbox{HE}_{IV}$ be the first, second, third and fourth type Loo-Keng Hua domain respectively, $\vp$ a holomorphic self-map of $\mbox{HE}_I$, $\mbox{HE}_{II}$, $\mbox{HE}_{III}$, or $\mbox{HE}_{IV}$ and $u\in H(\M)$ the space of all holomorphic functions on $\M\in\{\mbox{HE}_I, \mbox{HE}_{II}, \mbox{HE}_{III}, \mbox{HE}_{IV}\}$. In this paper, motivated by the well known Hua's matrix inequality, first some inequalities for the points in the Bers-type spaces of the Loo-Keng Hua domains are obtained, and then the boundedness and compactness of the weighted composition operators $W_{\vp,u}:f\mapsto u\cdot f\circ\vp$ on Bers-type spaces of these domains are characterized.
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참고문헌 (25)
참고문헌 신청
R. F. Allen / 2010 / Topics in operator theory. Volume 1. Operators, matrices and analytic functions / Birkhauser Verlag :11~37
Robert F. Allen / 2010 / Weighted Composition Operators from H ∞ to the Bloch Space of a Bounded Homogeneous Domain / Integral Equations and Operator Theory 66(1):21~40
Flavia Colonna / 2013 / Weighted Composition Operators from the Minimal Möbius Invariant Space into the Bloch Space / Mediterranean Journal of Mathematics 10(1):395~409
C. C. Cowen / 1995 / Composition operators on spaces of analytic functions, Studies in Advanced Mathematics / CRC Press
Kobra Esmaeili / 2013 / Weighted Composition Operators Between Zygmund Type Spaces and Their Essential Norms / Integral Equations and Operator Theory 75(4):473~490
Robert F. Allen / 2010 / Weighted Composition Operators from H ∞ to the Bloch Space of a Bounded Homogeneous Domain / Integral Equations and Operator Theory 66(1):21~40
Flavia Colonna / 2013 / Weighted Composition Operators from the Minimal Möbius Invariant Space into the Bloch Space / Mediterranean Journal of Mathematics 10(1):395~409
C. C. Cowen / 1995 / Composition operators on spaces of analytic functions, Studies in Advanced Mathematics / CRC Press
Kobra Esmaeili / 2013 / Weighted Composition Operators Between Zygmund Type Spaces and Their Essential Norms / Integral Equations and Operator Theory 75(4):473~490
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