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Hardy Spaces of Holomorphic Functions for Domains in ℂn with Minimal Smoothness

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Harmonic Analysis, Partial Differential Equations, Complex Analysis, Banach Spaces, and Operator Theory (Volume 1)

Part of the book series: Association for Women in Mathematics Series ((AWMS,volume 4))

Abstract

We prove various representations and density results for Hardy spaces of holomorphic functions for two classes of bounded domains in \(\mathbb{C}^{n}\), whose boundaries satisfy minimal regularity conditions (namely the classes C 2 and C 1, 1, respectively) together with naturally occurring notions of convexity.

Dedicated to the memory of Cora Sadosky

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Notes

  1. 1.

    Also known as the Szegő projection.

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Acknowledgements

Loredana Lanzani is supported in part by the National Science Foundation, awards DMS-1001304 and DMS-1503612. Elias M. Stein is supported in part by the National Science Foundation, awards DMS-0901040 and DMS-1265524.

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Authors and Affiliations

  1. Department of Mathematics, Syracuse University, Syracuse, NY, 13244-1150, USA

    Loredana Lanzani

  2. Department of Mathematics, Princeton University, Princeton, NJ, 08544-100, USA

    Elias M. Stein

Authors
  1. Loredana Lanzani
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  2. Elias M. Stein
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Correspondence to Loredana Lanzani .

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Editors and Affiliations

  1. Department of Mathematics and Statistics, University of New Mexico, Albuquerque, New Mexico, USA

    María Cristina Pereyra

  2. Department of Mathematics, Venezuelan Institute for Scientific Research, Caracas, Venezuela

    Stefania Marcantognini

  3. Department of Mathematical Sciences, Georgia Southern University, Statesboro, Georgia, USA

    Alexander M. Stokolos

  4. Department of Mathematics and Actu rial Science, Roosevelt University, Chicago, Illinois, USA

    Wilfredo Urbina

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Lanzani, L., Stein, E.M. (2016). Hardy Spaces of Holomorphic Functions for Domains in ℂn with Minimal Smoothness. In: Pereyra, M., Marcantognini, S., Stokolos, A., Urbina, W. (eds) Harmonic Analysis, Partial Differential Equations, Complex Analysis, Banach Spaces, and Operator Theory (Volume 1). Association for Women in Mathematics Series, vol 4. Springer, Cham. https://doi.org/10.1007/978-3-319-30961-3_11

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