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1. 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 |
2. CJM 2006 (vol 58 pp. 548)
Hausdorff and Quasi-Hausdorff Matrices on Spaces of Analytic Functions We consider Hausdorff and quasi-Hausdorff matrices as operators
on classical spaces of analytic functions such as the Hardy and
the Bergman spaces, the Dirichlet space, the Bloch spaces and $\BMOA$. When the generating
sequence of the matrix is the moment sequence of a measure $\mu$,
we find the conditions on $\mu$ which are equivalent to the boundedness
of the matrix on the various spaces.
Categories:47B38, 46E15, 40G05, 42A20 |
3. CJM 2000 (vol 52 pp. 468)
Two-Weight Estimates For Singular Integrals Defined On Spaces Of Homogeneous Type Two-weight inequalities of strong and weak type are obtained in the
context of spaces of homogeneous type. Various applications are
given, in particular to Cauchy singular integrals on regular curves.
Categories:47B38, 26D10 |
4. CJM 1997 (vol 49 pp. 100)
Multiplication Invariant Subspaces of Hardy Spaces This paper studies closed subspaces $L$
of the Hardy spaces $H^p$ which are $g$-invariant ({\it i.e.},
$g\cdot L \subseteq L)$ where $g$ is inner, $g\neq 1$. If
$p=2$, the Wold decomposition theorem implies that there is
a countable ``$g$-basis'' $f_1, f_2,\ldots$ of
$L$ in the sense that $L$ is a direct sum of spaces
$f_j\cdot H^2[g]$ where $H^2[g] = \{f\circ g \mid f\in H^2\}$.
The basis elements $f_j$ satisfy the
additional property that $\int_T |f_j|^2 g^k=0$,
$k=1,2,\ldots\,.$ We call such functions $g$-$2$-inner.
It also
follows that any $f\in H^2$ can be factored $f=h_{f,2}\cdot
(F_2\circ g)$ where $h_{f,2}$ is $g$-$2$-inner and $F$ is
outer, generalizing the classical Riesz factorization.
Using $L^p$ estimates for the canonical decomposition of
$H^2$, we find a factorization $f=h_{f,p} \cdot (F_p \circ
g)$ for $f\in H^p$. If $p\geq 1$ and $g$ is a finite
Blaschke product we obtain, for any $g$-invariant
$L\subseteq H^p$, a finite $g$-basis of $g$-$p$-inner
functions.
Categories:30H05, 46E15, 47B38 |