1. CJM 2011 (vol 63 pp. 862)
| 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)
|$Q_p$ 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
3. CJM 1997 (vol 49 pp. 55)
|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 $p=2$.