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Search: MSC category 32A37 ( Other spaces of holomorphic functions (e.g. bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA)) [See also 46Exx] )

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1. CMB 2013 (vol 57 pp. 794)

Fang, Zhong-Shan; Zhou, Ze-Hua
 New Characterizations of the Weighted Composition Operators Between Bloch Type Spaces in the Polydisk We give some new characterizations for compactness of weighted composition operators $uC_\varphi$ acting on Bloch-type spaces in terms of the power of the components of $\varphi,$ where $\varphi$ is a holomorphic self-map of the polydisk $\mathbb{D}^n,$ thus generalizing the results obtained by HyvÃ¤rinen and LindstrÃ¶m in 2012. Keywords:weighted composition operator, compactness, Bloch type spaces, polydisk, several complex variablesCategories:47B38, 47B33, 32A37, 45P05, 47G10

2. CMB 2001 (vol 44 pp. 150)

Jakóbczak, Piotr
 Exceptional Sets of Slices for Functions From the Bergman Space in the Ball Let $B_N$ be the unit ball in $\mathbb{C}^N$ and let $f$ be a function holomorphic and $L^2$-integrable in $B_N$. Denote by $E(B_N,f)$ the set of all slices of the form $\Pi =L\cap B_N$, where $L$ is a complex one-dimensional subspace of $\mathbb{C}^N$, for which $f|_{\Pi}$ is not $L^2$-integrable (with respect to the Lebesgue measure on $L$). Call this set the exceptional set for $f$. We give a characterization of exceptional sets which are closed in the natural topology of slices. Categories:32A37, 32A22

3. CMB 1999 (vol 42 pp. 97)

Kwon, E. G.
 On Analytic Functions of Bergman $\BMO$ in the Ball Let $B = B_n$ be the open unit ball of $\bbd C^n$ with volume measure $\nu$, $U = B_1$ and ${\cal B}$ be the Bloch space on $U$. ${\cal A}^{2, \alpha} (B)$, $1 \leq \alpha < \infty$, is defined as the set of holomorphic $f\colon B \rightarrow \bbd C$ for which $$\int_B \vert f(z) \vert^2 \left( \frac 1{\vert z\vert} \log \frac 1{1 - \vert z\vert } \right)^{-\alpha} \frac {d\nu (z)}{1-\vert z\vert} < \infty$$ if $0 < \alpha <\infty$ and ${\cal A}^{2, 1} (B) = H^2(B)$, the Hardy space. Our objective of this note is to characterize, in terms of the Bergman distance, those holomorphic $f\colon B \rightarrow U$ for which the composition operator $C_f \colon {\cal B} \rightarrow {\cal A}^{2, \alpha}(B)$ defined by $C_f (g) = g\circ f$, $g \in {\cal B}$, is bounded. Our result has a corollary that characterize the set of analytic functions of bounded mean oscillation with respect to the Bergman metric. Keywords:Bergman distance, \BMOA$, Hardy space, Bloch functionCategory:32A37 4. CMB 1998 (vol 41 pp. 129) Lee, Young Joo  Pluriharmonic symbols of commuting Toeplitz type operators on the weighted Bergman spaces A class of Toeplitz type operators acting on the weighted Bergman spaces of the unit ball in the$n\$-dimensional complex space is considered and two pluriharmonic symbols of commuting Toeplitz type operators are completely characterized. Keywords:Pluriharmonic functions, Weighted Bergman spaces, Toeplitz type operators.Categories:47B38, 32A37
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