Mathematics – Functional Analysis
Scientific paper
2005-03-31
Mathematics
Functional Analysis
24 Pages
Scientific paper
Let $U^{n}$ be the unit polydisc of ${\Bbb C}^{n}$ and $\phi=(\phi_1, >..., \phi_n)$ a holomorphic self-map of $U^{n}.$ By ${\cal B}^p(U^{n})$, ${\cal B}^p_{0}(U^{n})$ and ${\cal B}^p_{0*}(U^{n})$ denote the $p$-Bloch space, Little $p$-Bloch space and Little star $p$-Bloch space in the unit polydisc $U^n$ respectively, where $p, q>0$. This paper gives the estimates of the essential norms of bounded composition operators $C_{\phi}$ induced by $\phi$ between ${\cal B}^p(U^n)$ (${\cal B}^p_{0}(U^n)$ or ${\cal B}^p_{0*}(U^n)$) and ${\cal B}^q(U^n)$ (${\cal B}^q_{0}(U^n)$ or ${\cal B}^q_{0*}(U^n)$). As their applications, some necessary and sufficient conditions for the bounded composition operators $C_{\phi}$ to be compact from ${\cal B}^p(U^n)$ $({\cal B}^p_{0}(U^n)$ or ${\cal B}^p_{0*}(U^n))$ into ${\cal B}^q(U^n)$ (${\cal B}^q_{0}(U^n)$ or ${\cal B}^q_{0*}(U^n)$) are obtained.
Liu Yan
Zhou Zehua
No associations
LandOfFree
The Essential Norm of Composition Operator between Generalized Bloch Spaces in Polydiscs and its Applications does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The Essential Norm of Composition Operator between Generalized Bloch Spaces in Polydiscs and its Applications, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Essential Norm of Composition Operator between Generalized Bloch Spaces in Polydiscs and its Applications will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-721029