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arXiv · 1505.06511

Independent sums of $H^1_n(\mathbb{T})$ and $H^1_n(δ)$

Maciej Rzeszut·Michal Wojciechowski
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Abstract

We construct a new idempotent Fourier multiplier on the Hardy space on the bidisc, which could not be obtained by applying known one dimentional results. The main tool is a new $L^1$ equivalent of the Stein martingale inequality which holds for a special filtration of periodic subsets of $\mathbb{T}$ with some restrictions on the functions involved. We also identify the isomorphic type of the range of the associated operator as the independent sum of dyadic $H^1_n$, which is known to be a complemented and invariant subspace of dyadic $H^1$.

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Maciej Rzeszut, Michal Wojciechowski. 2016-06-14. Independent sums of $H^1_n(\mathbb{T})$ and $H^1_n(δ)$. https://arxiv.org/abs/1505.06511

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