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Factorization of Hardy spaces and Hankel operators on convex domains in ℂn

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Abstract

In this article we study the (small) Hankel operator hb on the Hardy and Bergman spaces on a smoothly bounded convex domain of finite type in ℂn. We completely characterize the Hankel operators hb that are bounded, compact, and belong to the Schatten ideal Sp, for 0 < p < ∞.

In particular, if hb denotes the Hankel operator on the Hardy space H2 (Ω), we prove that hb is bounded if and only if b ∈ BMOA, compact if and only if b ∈ VMOA, and in the Schatten class if and only if b ∈e Bp, 0 < p < ∞. This last result extends the analog theorem in the case of the unit disc of Peller [19] and Semmes [21].

In order to characterize the bounded Hankel operators, we prove a factorization theorem for functions in H1 (Ω), a result that is of independent interest.

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Authors and Affiliations

  1. Mapmo-Umr 6628, Département de Mathématiques, Université d’Orleans, 45067, Orléans Cedex 2, France

    Aline Bonami

  2. Dipartimento di Matematica, Politecnico de Torino, C. so Duca degli Abruzzi, 24, 10129, Torino, Italy

    Marco M. Peloso

  3. Upresa 6086 Groupes de Lie et Géométrie, Laboratoire de Mathématiques, Université de Poitiers, 86962, Futuroscope Chasseneuil Cedex, France

    Frédéric Symesak

Authors
  1. Aline Bonami
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  2. Marco M. Peloso
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  3. Frédéric Symesak
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Correspondence to Aline Bonami.

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Bonami, A., Peloso, M.M. & Symesak, F. Factorization of Hardy spaces and Hankel operators on convex domains in ℂn . J Geom Anal 11, 363–397 (2001). https://doi.org/10.1007/BF02922011

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  • DOI: https://doi.org/10.1007/BF02922011

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