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1. CJM 2012 (vol 65 pp. 299)
On Multilinear Fourier Multipliers of Limited Smoothness In this paper,
we prove certain $L^2$estimate
for multilinear Fourier multiplier operators
with multipliers of limited smoothness.
As a result,
we extend the result of CalderÃ³n and Torchinsky
in the linear theory to the multilinear case.
The sharpness of our results and some
related estimates in Hardy spaces
are also discussed.
Keywords:multilinear Fourier multipliers, HÃ¶rmander multiplier theorem, Hardy spaces Categories:42B15, 42B20 
2. 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 
3. CJM 2010 (vol 62 pp. 961)
Multiplicative Isometries and Isometric ZeroDivisors
For some Banach spaces of analytic functions in the unit disk
(weighted Bergman spaces, Bloch space, Dirichlettype spaces), the
isometric pointwise multipliers are found to be unimodular constants.
As a consequence, it is shown that none of those spaces have isometric
zerodivisors. Isometric coefficient multipliers are also
investigated.
Keywords:Banach spaces of analytic functions, Hardy spaces, Bergman spaces, Bloch space, Dirichlet space, Dirichlettype spaces, pointwise multipliers, coefficient multipliers, isometries, isometric zerodivisors Categories:30H05, 46E15 
4. 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 
5. CJM 2009 (vol 62 pp. 202)
Interior $h^1$ Estimates for Parabolic Equations with $\operatorname{LMO}$ Coefficients In this paper we establish
\emph{a priori} $h^1$estimates in a bounded domain for parabolic
equations with vanishing $\operatorname{LMO}$ coefficients.
Keywords:parabolic operator, Hardy space, parabolic, singular integrals and commutators Categories:35K20, 35B65, 35R05 
6. CJM 2003 (vol 55 pp. 1264)
Admissible Majorants for Model Subspaces of $H^2$, Part II: Fast Winding of the Generating Inner Function 
Admissible Majorants for Model Subspaces of $H^2$, Part II: Fast Winding of the Generating Inner Function This paper is a continuation of \cite{HM02I}. We consider the model
subspaces $K_\Theta=H^2\ominus\Theta H^2$ of the Hardy space $H^2$
generated by an inner function $\Theta$ in the upper half plane. Our
main object is the class of admissible majorants for $K_\Theta$,
denoted by $\Adm \Theta$ and consisting of all functions $\omega$
defined on $\mathbb{R}$ such that there exists an $f \ne 0$, $f \in
K_\Theta$ satisfying $f(x)\leq\omega(x)$ almost everywhere on
$\mathbb{R}$. Firstly, using some simple Hilbert transform techniques,
we obtain a general multiplier theorem applicable to any $K_\Theta$
generated by a meromorphic inner function. In contrast with
\cite{HM02I}, we consider the generating functions $\Theta$ such that
the unit vector $\Theta(x)$ winds up fast as $x$ grows from $\infty$
to $\infty$. In particular, we consider $\Theta=B$ where $B$ is a
Blaschke product with ``horizontal'' zeros, {\it i.e.}, almost
uniformly distributed in a strip parallel to and separated from $\mathbb{R}$.
It is shown, among other things, that for any such $B$, any even
$\omega$ decreasing on $(0,\infty)$ with a finite logarithmic integral
is in $\Adm B$ (unlike the ``vertical'' case treated in \cite{HM02I}),
thus generalizing (with a new proof) a classical result related to
$\Adm\exp(i\sigma z)$, $\sigma>0$. Some oscillating $\omega$'s in
$\Adm B$ are also described. Our theme is related to the
BeurlingMalliavin multiplier theorem devoted to $\Adm\exp(i\sigma z)$,
$\sigma>0$, and to de~Branges' space $\mathcal{H}(E)$.
Keywords:Hardy space, inner function, shift operator, model, subspace, Hilbert transform, admissible majorant Categories:30D55, 47A15 
7. CJM 2003 (vol 55 pp. 1231)
Admissible Majorants for Model Subspaces of $H^2$, Part I: Slow Winding of the Generating Inner Function 
Admissible Majorants for Model Subspaces of $H^2$, Part I: Slow Winding of the Generating Inner Function A model subspace $K_\Theta$ of the Hardy space $H^2 = H^2
(\mathbb{C}_+)$ for the upper half plane $\mathbb{C}_+$ is
$H^2(\mathbb{C}_+) \ominus \Theta H^2(\mathbb{C}_+)$ where $\Theta$
is an inner function in $\mathbb{C}_+$. A function $\omega \colon
\mathbb{R}\mapsto[0,\infty)$ is called {\it an admissible
majorant\/} for $K_\Theta$ if there exists an $f \in K_\Theta$, $f
\not\equiv 0$, $f(x)\leq \omega(x)$ almost everywhere on
$\mathbb{R}$. For some (mainly meromorphic) $\Theta$'s some parts
of $\Adm\Theta$ (the set of all admissible majorants for
$K_\Theta$) are explicitly described. These descriptions depend on
the rate of growth of $\arg \Theta$ along $\mathbb{R}$. This paper
is about slowly growing arguments (slower than $x$). Our results
exhibit the dependence of $\Adm B$ on the geometry of the zeros of
the Blaschke product $B$. A complete description of $\Adm B$ is
obtained for $B$'s with purely imaginary (``vertical'') zeros. We
show that in this case a unique minimal admissible majorant exists.
Keywords:Hardy space, inner function, shift operator, model, subspace, Hilbert transform, admissible majorant Categories:30D55, 47A15 
8. CJM 1998 (vol 50 pp. 897)
Fourier multipliers for local hardy spaces on ChÃ©bliTrimÃ¨che hypergroups In this paper we consider Fourier multipliers on local
Hardy spaces $\qin$ $(0
