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Rigidity of Volterra-type integral operators on Hardy spaces of the unit ball

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 نشر من قبل Antti Per\\\"al\\\"a
 تاريخ النشر 2020
  مجال البحث
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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 $p e 2.$



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