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1. 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 |
2. CJM 2009 (vol 62 pp. 415)
Classification of Reducing Subspaces of a Class of Multiplication Operators on the Bergman Space via the Hardy Space of the Bidisk |
Classification of Reducing Subspaces of a Class of Multiplication Operators on the Bergman Space via the Hardy Space of the Bidisk In this paper we obtain a complete description of nontrivial minimal reducing subspaces of the multiplication operator by a Blaschke product with four zeros on the Bergman space of the unit disk via the Hardy space of the bidisk.
Categories:47B35, 47B38 |
3. CJM 2009 (vol 61 pp. 190)
Bounded Hankel Products on the Bergman Space of the Polydisk We consider the problem of determining for which square integrable
functions $f$ and $g$ on the polydisk the densely defined Hankel
product $H_{f}H_g^\ast$ is bounded on the Bergman space of the
polydisk. Furthermore, we obtain similar results for the mixed
Haplitz products $H_{g}T_{\bar{f}}$ and $T_{f}H_{g}^{*}$, where $f$
and $g$ are square integrable on the polydisk and $f$ is analytic.
Keywords:Toeplitz operator, Hankel operator, Haplitz products, Bergman space, polydisk Categories:47B35, 47B47 |
4. CJM 2003 (vol 55 pp. 379)
Generalized Factorization in Hardy Spaces and the Commutant of Toeplitz Operators Every classical inner function $\varphi$ in the unit disk gives rise to
a certain factorization of functions in Hardy spaces. This factorization,
which we call the generalized Riesz factorization, coincides with the
classical Riesz factorization when $\varphi(z)=z$. In this paper we prove
several results about the generalized Riesz factorization, and we apply
this factorization theory to obtain a new description of the commutant
of analytic Toeplitz operators with inner symbols on a Hardy space. We
also discuss several related issues in the context of the Bergman space.
Categories:47B35, 30D55, 47A15 |
5. CJM 1999 (vol 51 pp. 850)
Tensor Algebras, Induced Representations, and the Wold Decomposition Our objective in this sequel to \cite{MSp96a} is to develop extensions,
to representations of tensor algebras over $C^{*}$-correspondences, of
two fundamental facts about isometries on Hilbert space: The Wold
decomposition theorem and Beurling's theorem, and to apply these to
the analysis of the invariant subspace structure of certain subalgebras
of Cuntz-Krieger algebras.
Keywords:tensor algebras, correspondence, induced representation, Wold decomposition, Beurling's theorem Categories:46L05, 46L40, 46L89, 47D15, 47D25, 46M10, 46M99, 47A20, 47A45, 47B35 |
6. CJM 1998 (vol 50 pp. 658)
Hankel operators on pseudoconvex domains of finite type in ${\Bbb C}^2$ The aim of this paper is to study small Hankel operators $h$ on the
Hardy space or on weighted Bergman spaces, where $\Omega$ is a
finite type domain in ${\Bbbvii C}^2$ or a strictly pseudoconvex
domain in ${\Bbbvii C}^n$. We give a sufficient condition on the
symbol $f$ so that $h$ belongs to the Schatten class ${\cal S}_p$,
$1\le p<+\infty$.
Categories:32A37, 47B35, 47B10, 46E22 |