A note on inhomogeneous Besov space associated with sections

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黃冠傑(Kuan-Chieh Huang) 查詢紙本館藏

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(A note on inhomogeneous Besov space associated with sections)

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摘要(中)

在這篇文章中，我們考慮在R上的函數Φ(x) = (x^2)/2，那麼可以得到擬度量ρ(x, y) = ((x-y)^2)/2 和 section。我們證明了如果R上的任意兩點x, y 滿足ρ(x, y)≧ 1 時就有|D_0HD_0|≦Cρ(x, y)^(-1)的話，則Monge–Ampère 奇異積分算子 H 在關於 section 的非齊次的 Besov 空間是有界的。

摘要(英)

In this paper, we considerΦ(x) = (x^2)/2 on R. Then we haveρ(x, y) = ((x-y)^2)/2 and the section. We show that the Monge–Ampère singular integral operator H is bounded on be the inhomogeneous Besov space associated with these sections if |D_0HD_0|≦Cρ(x, y)^(-1) for any x, y in R, ρ(x, y)≧ 1.

關鍵字(中)

★ Monge–Ampère 奇異積分算子

關鍵字(英)

★ Besov space
★ Monge–Ampère singular integral operator

論文目次

CONTENTS
摘要 i
Abstract ii
Contents iii
1 Introduction and Main theorem 1
2 Preliminaries 4
3 Proof of main theorem 7
References 18

參考文獻

References
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[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. Gutiérrez, Realanalysis related to the Monge–Ampère equation, Trans. Amer. Math. Soc. 348 (1996), 1075-1092.
[4] L. A. Caffarelli and C. E. Gutiérrez, Properties of the solutions of the linearized Monge-Amp ere equation, 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, Wavelet Theory and Harmonic Analysis in Applied Sciences(Buenos Aires, 1995), 3-13, C. A. D′Atellis and E. M. Fernandez-Berdaguer, Eds., Appl. Numer. Harmon. Anal., Birkhauser Boston, Boston, MA, 1997.
[6] Y. Ding and C.-C. Lin, Hardy space sassociated to the sections, Tôhoku Math. J. 57 (2005), 147-170.
[7] Y.S. Han, Inhomogeneous Calderón reproducing formula on spaces of homogeneous type, J. Geom. Anal. 7(1997), 259-284.
[8] Y.S. Han and D.C. Yang, Some new space of Besov and Triebel-Lizorking type on homogeneous spaces, Studia Mathemtica 156 (1)(2003).
[9] Y.S. Han, S.Z. Lu and D.C. Yang, Inhomogeneous Besov and Triebel-Lizorking spaces on spaces of homogeneous type, Approx. theory and its appl. 15:3, (1993), 37-65.
[10] A. Incognito, Weak-type (1, 1) inequality for the Monge–Ampère SIO′s, J. Fourier Anal. Appl. 7 (2001), 41-48.
[11] M.-Y. Lee, The boundedness of Monge–Ampère singular integral operators, J. Fourier Anal. Appl. 18 (2012), 211-222.
[12] C.-C. Lin, Boundedness of Monge–Ampère singular integral operators acting on Hardy spaces and their duals, Trans. Amer. Math. Soc., 368(2015), 3075-3104.

指導教授

李明憶

審核日期

2017-7-7

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