Thursday, September 28, 2017 - 15:00 to 15:50

427 Thackeray

### Abstract or Additional Information

We prove fact that the projection $\tilde{P}_m$ onto the subspace $\tilde{V}_m$ of $L_2\left(\mathbb{T}^\infty\right)$

spanned by functions dependent on at most $m$ variables is bounded on the space $H^1\left(\mathbb{D}^\infty\right)$

of functions in $L^1\left(\mathbb{T}^\infty\right)$ analytic in each variable, with norm $\leq c^m$.

As a byproduct we get another proof the Bourgain-Kwapień theorem. We also prove that $\tilde{P}_2$ acts on

the martingale Hardy space associated with a certain double-indexed filtration.