Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Independent sums of $H^1_n(\mathbb{T})$ and $H^1_n(\delta)$   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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The categories of this paper are: q-bio
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The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: econ
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The categories of this paper are: cond-mat
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The categories of this paper are: quant-ph
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The categories of this paper are: cs
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The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
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The categories of this paper are: stat