1. CJM 2011 (vol 64 pp. 1329)
||Composition Operators Induced by Analytic Maps to the Polydisk|
We study properties of composition operators
induced by symbols acting from the unit disk to the polydisk.
This result will be involved in the investigation
of weighted composition operators on the Hardy space on the unit disk
and moreover be concerned with composition operators acting
from the Bergman space to the Hardy space on the unit disk.
Keywords:composition operators, Hardy spaces, polydisk
Categories:47B33, 32A35, 30H10
2. CJM 2009 (vol 62 pp. 439)
||On Hankel Forms of Higher Weights: The Case of Hardy Spaces|
In this paper we study bilinear Hankel forms of higher weights on Hardy spaces in several dimensions. (The Schatten class Hankel forms of higher weights on weighted Bergman spaces have already been studied by Janson and Peetre for one dimension and by SundhÃ¤ll for several dimensions). We get a full characterization of Schatten class Hankel forms in terms of conditions for the symbols to be in certain Besov spaces. Also, the Hankel forms are bounded and compact if and only if the symbols satisfy certain Carleson measure criteria and vanishing Carleson measure criteria, respectively.
Keywords:Hankel forms, Schattenâvon Neumann classes, Bergman spaces, Hardy spaces, Besov spaces, transvectant, unitary representations, MÃ¶bius group
Categories:32A25, 32A35, 32A37, 47B35
3. CJM 1998 (vol 50 pp. 99)
||$A_\phi$-invariant subspaces on the torus |
Generalizing the notion of invariant subspaces on
the 2-dimensional torus $T^2$, we study the structure
of $A_\phi$-invariant subspaces of $L^2(T^2)$. A
complete description is given of $A_\phi$-invariant
subspaces that satisfy conditions similar to those
studied by Mandrekar, Nakazi, and Takahashi.
4. CJM 1997 (vol 49 pp. 653)