Abstract
The purpose of this note is to describe some results of real analysis related with the Monge-Ampère equation that are proved in [1] and to show its application to the boundedness of certain singular integrals.
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References
L. A. Caffarelli and C. E. Gutiérrez Real Analysis Related to the Monge-Ampère Equation. Trans. A. M. S.,vol 348(3): 1075–1092, 1996.
L. A. Caffarelli Some Regularity Properties of Solutions of Monge-Ampère Equation. Comm. on Pure and App. Math.,vol XLIV: 965–969, 1991.
L. A. Caffarelli and C. E. Gutiérrez Properties of the Solutions of the Linearized Monge-Ampère Equation. to appear in Amer. Jour of Math.
E. M. Stein Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals Princeton Math. Series #43, Princeton U. Press, Princeton, NJ, 1993.
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Caffarelli, L.A., Gutiérrez, C.E. (1997). Singular integrals related to the Monge-Ampère equation. In: D’Attellis, C.E., Fernández-Berdaguer, E.M. (eds) Wavelet Theory and Harmonic Analysis in Applied Sciences. Applied and Numerical Harmonic Analysis. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-2010-7_1
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DOI: https://doi.org/10.1007/978-1-4612-2010-7_1
Publisher Name: Birkhäuser, Boston, MA
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