Title: Weak Factorization of Hardy spaces on the polydisk
A classical result in the theory of Hardy spaces on the unit disc $
\mathbb{D}$ says that for any $0 < p,r,s < \infty$ satisfying
$\frac{1}{r} + \frac{1}{s} = \frac{1}{p}$, each $f \in H^p(\mathbb{D})$,
$f$ may be factorized as $f = g h$, where $g \in H^s(\mathbb{D})$, $h \in
H^r(\mathbb{D})$.
The situation in the case of the Hardy spaces on the polydisc
$\mathbb{D}^n$, so-called product Hardy spaces,
is much more subtle. A direct factorization into two functions cannot
be expected here. We look instead at weak factorisation properties, which
can be expressed on the dual side as boundedness
properties of Hankel operators on product Hardy spaces. The case $p=1$ was
finally solved by Ferguson, Lacey and Terwilleger in
2002 and 2007. In the talk, I shall present new factorization results for
the case $\frac{1}{2} \le p \le \frac{3}{2}$.
This is joint work with Aline Bonami, Benoit Sehba and Brett Wick.