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 我們討論的是在R上，用ϕ(x) = x2造出Sϕ(x, t) = B(x, √t)這個section，而B(x, √t)是一個以x為中心，以√t為半徑的開區間。最後我們用這個section 造出一個Monge-Ap`ere奇異積分算子。
 Let ϕ(x) = x2 be a strictly convex and smooth function on R, we construct Sϕ(x, t) = B(x, √t), where B(x, √t) is a open interval with center x and radius √t. Then the section Sϕ satisﬁes the condition of section. we also construct an example of the Monge-Ap`ere singular integral operator.
 摘要 iAbstract iiContents iii1. Introduction 12. Properties of the section 23. Construction of the Monge-Amp`ere singular integral operator 7References 11
 [1] L. A. Caﬀarelli, Some regularity properties of solutions of Monge-Amp`ere equation, Comm. PureAppl. Math. XLIV (1991), 965–969.[2] L. A. Caﬀarelli, Boundary regularity of maps with convex potentials, Comm. Pure Appl. Math. XLV(1992), 1141–1151.[3] L. A. Caﬀarelli and C. E. Guti´errez, Real analysis related to the Monge-Amp`ere equation, Trans.Amer. Math. Soc. 348 (1996), 1075–1092.[4] L. A. Caﬀarelli and C. E. Guti´errez, Properties of the solutions of the linearized Monge-Amp`ereequation, Amer. J. Math. 119 (1997), 423–465.[5] L. A. Caﬀarelli and C. E. Guti´errez, Singular integrals related to the Monge-Amp`ere equation, WaveletTheory and Harmonic Analysis in Applied Sciences (Buenos Aires, 1995), 3–13, C. A. D’Atellis andE. M. Fernandez-Berdaguer, Eds., Appl. Numer. Harmon. Anal., Birkh¨auser Boston, Boston, MA,1997.
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