A note on inhomogeneous Triebel-Lizorkin space associated with sections

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林靖容(Jing-Rong Lin) 查詢紙本館藏

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論文名稱

(A note on inhomogeneous Triebel-Lizorkin space associated with sections)

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摘要(中)

在這篇文章中，我們討論R^n上特定的section，就是固定x為中心、以√t為半徑的球體B(x,√t)，其勒貝格測度等價於t^(n/2)，因此可以考慮關於此section的非齊性F_pq^s (R^n )，當任意兩點x,y滿足|x-y|≥1時，Monge-Ampère奇異積分算子H有|D_0 HD_0 (x,y)|≤|x-y|^(-2)的條件，即可證明H在F_pq^s (R^n )上有界。

摘要(英)

In this paper, we consider the special section on R^n, which is a ball centered at with radius √t, and the Lesbegue measure of this section is equivalent to t^(n/2). Then, define the inhomogenous Triebel-Lizorkin space F_pq^s (R^n ) associated with such sections, and show that the Monge-Ampère singular integral operator H is bounded on F_pq^s (R^n ) if |D_0 HD_0 (x,y)|≤|x-y|^(-2) for any x,y∈R^n,|x-y|≥1.

關鍵字(中)

★ Triebel-Lizorkin space
★ sections

關鍵字(英)

論文目次

摘要 i
Abstract ii
Contents iii
1 Introduction 1
2 Preliminaries 4
3 Pointwise orthogonality estimate 8
4 Proof of Theorem 1.1 13
Appendice 19
References 20

參考文獻

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[3] L. A. Caffarelli and C. E. Gutiérrez, Real analysis related to the Monge–Ampère equatio. Trans. Amer. Math. Soc. 348 (1996), no. 3, 1075-1092.
[4] L. A. Caffarelli and C. E. Gutiérrez, Properties of the solutions of the linearized Monge–Ampère equation. Amer. J. Math. 119 (1997), no. 2, 423-465.
[5] L. A. Caffarelli and C. E. Gutiérrez, Singular integrals related to the Monge–Ampère 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., Birkhäuser Boston, Boston, MA, 1997.
[6] Y. Ding and C.-C. Lin, Hardy spaces associated to the sections. Tohoku Math. J. 57 (2005), no. 2, 147-170.
[7] C. Fefferman, E. M. Stein, Some maximal inequalities, Amer. J. Math. 93 (1971), 107-116.
[8] Y.-S. Han, Inhomogeneous Calderón reproducing formula on spaces of homogeneous type, J. Geom. Anal. 7 (1997), 259-284.
[9] Y.-S. Han, M.-Y. Lee, C.-C. Lin, Boundedness of Monge–Ampère singular integral operators on Besov spaces, Appl. Analysis, published online.
https://cats.informa.com/PTS/in?t=lop&m=1549322&op=2
[10] Y.-S. Han, D.-C. Yang, Some new space of Besov and Triebel-Lizorking type on homogeneous spaces, Studia Mathematica 156 (1)(2003).
[11] A. Incognito, Weak-type (1,1) inequality for the Monge–Ampère SIO’s, J. Fourier Anal. Appl. 7 (2001), 41-48.
[12] M.-Y. Lee, The boundedness of Monge–Ampère singular integral operators, J. Fourier Anal. Appl. 18 (2012), 211-222.
[13] C.-C. Lin, Boundedness of Monge–Ampère singular integral operators acting on Hardy spaces and their duals, Tran. Amer. Math. Soc., 368(2015), 3075-3104.

指導教授

李明憶(Ming-Yi Lee)

審核日期

2019-1-14

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