This is an announcement for the paper "A weak-type inequality for non-commutative martingales and applications" by Narcisse Randrianantoanina. Abstract: We prove a weak-type (1,1) inequality for square functions of non-commutative martingales that are simultaneously bounded in $L^2$ and $L^1$. More precisely, the following non-commutative analogue of a classical result of Burkholder holds: there exists an absolute constant $K>0$ such that if $\cal{M}$ is a semi-finite von Neumann algebra and $(\cal{M}_n)^{\infty}_{n=1}$ is an increasing filtration of von Neumann subalgebras of $\cal{M}$ then for any given martingale $x=(x_n)^{\infty}_{n=1}$ that is bounded in $L^2(\cal{M})\cap L^1(\cal{M})$, adapted to $(\cal{M}_n)^{\infty}_{n=1}$, there exist two \underline{martingale difference} sequences, $a=(a_n)_{n=1}^\infty$ and $b=(b_n)_{n=1}^\infty$, with $dx_n = a_n + b_n$ for every $n\geq 1$, \[ \left\| \left(\sum^\infty_{n=1} a_n^*a_n \right)^{{1}/{2}}\right\|_{2} + \left\| \left(\sum^\infty_{n=1} b_nb_n^*\right)^{1/2}\right\|_{2} \leq 2\left\| x \right\|_2, \] and \[ \left\| \left(\sum^\infty_{n=1} a_n^*a_n \right)^{{1}/{2}}\right\|_{1,\infty} + \left\| \left(\sum^\infty_{n=1} b_nb_n^*\right)^{1/2}\right\|_{1,\infty} \leq K\left\| x \right\|_1. \] As an application, we obtain the optimal orders of growth for the constants involved in the Pisier-Xu non-commutative analogue of the classical Burkholder-Gundy inequalities. Archive classification: Functional Analysis; Operator Algebras Mathematics Subject Classification: 46L53, 46L52 Remarks: 38 pages The source file(s), weaktype4.tex: 108231 bytes, is(are) stored in gzipped form as 0409139.gz with size 30kb. The corresponding postcript file has gzipped size 137kb. Submitted from: randrin@muohio.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0409139 or http://arXiv.org/abs/math.FA/0409139 or by email in unzipped form by transmitting an empty message with subject line uget 0409139 or in gzipped form by using subject line get 0409139 to: math@arXiv.org.