This is an announcement for the paper “Factorization in mixed norm Hardy and BMO spaces” by Richard Lechnerhttps://arxiv.org/find/math/1/au:+Lechner_R/0/1/0/all/0/1.

Abstract: Let $1\leq p, q<\infty$ and $1\leq r\leq\infty$. We show that the direct sum of mixed norm Hardy spaces $(\sum_n H_n^p(H_n^q))_r$ and the sum of their dual spaces $(\sum_n H_n^p(H_n^q)^*)_r$ are both primary. We do so by using Bourgain's localization method and solving the finite dimensional factorization problem. In particular, we obtain that the spaces $(\sum_n H_n^1(H_n^s))_r, (\sum_n H_n^1(H_n^s))_r)$, as well as $(\sum_n BMO_n(H_n^s))_r$ and $(\sum_n H_n^s(BMO_n))_r$, $1<s<\infty, 1\leq r\leq\infty$ are all primary..

The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1610.01506