Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rigidity of Volterra-type integral operators on Hardy spaces of the unit
  ball   We establish that the Volterra-type integral operator $J_b$ on the Hardy
spaces $H^p$ of the unit ball $\mathbb{B}_n$ exhibits a rather strong rigid
behavior. More precisely, we show that the compactness, strict singularity and
$\ell^p$-singularity of $J_b$ are equivalent on $H^p$ for any $1 \le p <
\infty$. Moreover, we show that the operator $J_b$ acting on $H^p$ cannot fix
an isomorphic copy of $\ell^2$ when $p \ne 2.$

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The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org
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The categories of this paper are: funct-an
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The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
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The categories of this paper are: chem-ph
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The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
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The categories of this paper are: econ
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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas