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The Boundedness of Monge-Ampère Singular Integral Operators

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Abstract

We first define molecules for Hardy spaces \(H^{1}_{\mathcal{F}}(\mathbb{R}^{n})\) associated with a family \(\mathcal{F}\) of sections which is closely related to the Monge-Ampère equation and prove their molecular characters. As an application, we show that Monge-Ampère singular operators are bounded on \(H^{1}_{\mathcal{F}}(\mathbb{R}^{n})\).

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Authors and Affiliations

  1. Department of Mathematics, National Central University, Chung-Li, 320, Taiwan, Republic of China

    Ming-Yi Lee

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  1. Ming-Yi Lee
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Correspondence to Ming-Yi Lee.

Additional information

Communicated by Fernando Soria.

Research was supported by NSC of Taiwan under Grant #NSC 99-2115-M-008-002-MY3.

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Lee, MY. The Boundedness of Monge-Ampère Singular Integral Operators. J Fourier Anal Appl 18, 211–222 (2012). https://doi.org/10.1007/s00041-011-9203-4

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  • DOI: https://doi.org/10.1007/s00041-011-9203-4

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