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On Supnorm Estimates for \(\bar{\partial}\) on Infinite Type Convex Domains in ℂ2

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Abstract

In this paper, we study the \(\bar{\partial}\) equation on some convex domains of infinite type in ℂ2. In detail, we prove that supnorm estimates hold for infinite exponential type domains, provided the exponent is less than 1.

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Authors and Affiliations

  1. Mathematics Department, The University of Michigan, East Hall, Ann Arbor, MI, 48109, USA

    John Erik Fornæss & Lina Lee

  2. Mathematics Department, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA, 92093, USA

    Yuan Zhang

Authors
  1. John Erik Fornæss
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  2. Lina Lee
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  3. Yuan Zhang
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Corresponding author

Correspondence to Lina Lee.

Additional information

Communicated by Steve Bell.

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Fornæss, J.E., Lee, L. & Zhang, Y. On Supnorm Estimates for \(\bar{\partial}\) on Infinite Type Convex Domains in ℂ2 . J Geom Anal 21, 495–512 (2011). https://doi.org/10.1007/s12220-010-9155-y

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  • DOI: https://doi.org/10.1007/s12220-010-9155-y

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