Instytut Matematyczny Polskiej Akademii Nauk / pl / Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

Streszczenie

\tolerance 6000Let $1\leq p,q \lt \infty$ and $1\leq r \leq \infty$. We show that the direct sum $(\sum_n H^p_n(H^q_n))_r$ of the mixed norm Hardy spaces and the sum $(\sum_n H^p_n(H^q_n)^*)_r$ of their dual spaces are both primary. We do so by using Bourgain’s localization method and solving the finite-dimensional factorization problem. In particular, we show that the spaces $(\sum_{n\in \mathbb N} H_n^1(H_n^s))_r$, $(\sum_{n\in \mathbb N} H_n^s(H_n^1))_r$, as well as $(\sum_{n\in \mathbb N} {\mathrm {BMO}}_n(H_n^s))_r$ and $(\sum_{n\in \mathbb N} H^s_n( {\mathrm {BMO}}_n))_r$, $1 \lt s \lt \infty$, $1\leq r \leq \infty$, are all primary.