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Existence and Interior Regularity Theorems for \(\bar{\partial }\) on Q-Convex Domains

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Abstract

We establish for a q-convex domain \(\Omega \subset {{\mathbb {C}}}^n \) existence results in \(L^2_{p,k-1}(\Omega ,\text {loc})\) and \(C_{p,k-1}^\infty (\Omega )\) for the equation \(\bar{\partial }\textit{u}=f\), where f is a (p, k)-form on \(\Omega \) of degree \(k\ge q\) such that \(\bar{\partial }\textit{f}=0\).

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Authors and Affiliations

  1. Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, IL, 61801, USA

    Martino Fassina

  2. Department of Mathematics, University of Padova, via Trieste 63, Padova, Italy

    Stefano Pinton

Authors
  1. Martino Fassina
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  2. Stefano Pinton
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Correspondence to Stefano Pinton.

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Communicated by Irene Sabadini.

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Fassina, M., Pinton, S. Existence and Interior Regularity Theorems for \(\bar{\partial }\) on Q-Convex Domains. Complex Anal. Oper. Theory 13, 2487–2494 (2019). https://doi.org/10.1007/s11785-018-0874-6

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  • DOI: https://doi.org/10.1007/s11785-018-0874-6

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