Canadian Mathematical Society
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Search: MSC category 30D45 ( Bloch functions, normal functions, normal families )

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1. CJM 2011 (vol 63 pp. 862)

Hosokawa, Takuya; Nieminen, Pekka J.; Ohno, Shûichi
Linear Combinations of Composition Operators on the Bloch Spaces
We characterize the compactness of linear combinations of analytic composition operators on the Bloch space. We also study their boundedness and compactness on the little Bloch space.

Keywords: composition operator, compactness, Bloch space
Categories:47B33, 30D45, 47B07

2. CJM 1998 (vol 50 pp. 449)

Aulaskari, Rauno; He, Yuzan; Ristioja, Juha; Zhao, Ruhan
$Q_p$ spaces on Riemann surfaces
We study the function spaces $Q_p(R)$ defined on a Riemann surface $R$, which were earlier introduced in the unit disk of the complex plane. The nesting property $Q_p(R)\subseteq Q_q(R)$ for $0
Categories:30D45, 30D50, 30F35

3. CJM 1997 (vol 49 pp. 55)

Chen, Huaihui; Gauthier, Paul M.
Normal Functions: $L^p$ Estimates
For a meromorphic (or harmonic) function $f$, let us call the dilation of $f$ at $z$ the ratio of the (spherical) metric at $f(z)$ and the (hyperbolic) metric at $z$. Inequalities are known which estimate the $\sup$ norm of the dilation in terms of its $L^p$ norm, for $p>2$, while capitalizing on the symmetries of $f$. In the present paper we weaken the hypothesis by showing that such estimates persist even if the $L^p$ norms are taken only over the set of $z$ on which $f$ takes values in a fixed spherical disk. Naturally, the bigger the disk, the better the estimate. Also, We give estimates for holomorphic functions without zeros and for harmonic functions in the case that $p=2$.

Categories:30D45, 30F35

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