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Solution of the \(\partial {\bar{\partial }}\)-problem in a pseudoconvex domain of \({{\mathbb {C}}}^n\)

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Abstract

We solve the \(\partial {\bar{\partial }}\) for the extendable currents and for the differential forms admitting a boundary value in currents sense in the case of a pseudoconvex domain with smooth boundary of class \(C^\infty \) of \({\mathbb {C}}^n\) and the \(\partial {\bar{\partial }}\) for the extendable currents defined on a strictly pseudoconvex domain with piecewise smooth boundary of \({\mathbb {C}}^n\).

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Author notes

  1. Souhaibou Sambou and Eramane Bodian are co-first authors, they contributed equally to this work.

  2. Winnie Ossete Ingoba and Ibrahima Hamidine are co-second authors, they contributed equally.

Authors and Affiliations

  1. Department of Mathematics UFR of Sciences and Technologies, University Assane Seck of Ziguinchor, BP: 523, Ziguinchor, Senegal

    Souhaibou Sambou, Eramane Bodian & Winnie Ossete Ingoba

  2. Department of Mathematics and Computer Science Faculty of Science and Technology, Abdou Moumouni University, BP: 10662, Niamey, Niger

    Ibrahima Hamidine

Authors
  1. Souhaibou Sambou
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  2. Eramane Bodian
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  3. Winnie Ossete Ingoba
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  4. Ibrahima Hamidine
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Correspondence to Eramane Bodian.

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Communicated by Samy Ponnusamy.

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Sambou, S., Bodian, E., Ingoba, W.O. et al. Solution of the \(\partial {\bar{\partial }}\)-problem in a pseudoconvex domain of \({{\mathbb {C}}}^n\). J Anal 30, 1361–1375 (2022). https://doi.org/10.1007/s41478-022-00385-2

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  • DOI: https://doi.org/10.1007/s41478-022-00385-2

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