關於加權哈弟空間結合仿增長函數的一個註解

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蔡孟軒(Meng-Shuan Tsai) 查詢紙本館藏

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論文名稱

關於加權哈弟空間結合仿增長函數的一個註解
(A Note on Weighted Hardy Spaces Associated to Para-accretive Functions)

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摘要(中)

在本文中，我們證明一個結合了仿增長函數的加權哈弟空間Hpb,w的子空間，它的一個新的原子分解，藉此得到一個線性算子有界性的檢定法。在應用上，利用到消失矩條件，我們證明某些種類的Calderon－Zygmund算子在Hpb,w空間上是有界的。

摘要(英)

In this article, we prove a new atomic decomposition for the subspace of weight Hardy space associated to para-accretive function Hpb,w and then obtain a criterion of the boundedness of linear operator. As an application, we show some kinds of Calderon-Zygmund operators are bounded on Hpb,w under some vanishing condition.

關鍵字(中)

★ 原子分解
★ Calderon-Zygmund算子
★ 哈弟空間
★ Plancherel-Polya不等式
★ Calderon型再生公式

關鍵字(英)

★ Plancherel-Polya inequality
★ Calderon-type reproducing formula
★ Hardy space
★ Calderon-Zygmund operators
★ Atomic decomposition

論文目次

中文摘要.................................................i
英文摘要.................................................ii
致謝辭.................................................iii
目錄.....................................................v
1. Introduction..........................................2
2. Preliminaries.........................................3
3. A new atomic decomposition of M^(ε,ε,b)...............9
4. Boundedness of Calderon-Zygmund operators on Hpb,w....14
References...............................................20

參考文獻

[1] W. Chen, Y. Han, C. Miao, A note on the boundedness of Calderon-Zygmund operators on Hardy spaces, J. Math. Anal. Appl. 310 (2005), no.1, 57-67.
[2] D. David, J. L. Journe and S. Semmes, Operateurs de Calderon-Zygmund, fonctions para-accretives et interpolation, Rev. Mat. Iberoamericana, 1 (1985), 1-56.
[3] J. Garcia-Cuerva and J. Rubio de Francia, Weighted Norm Inequalities and Related Topics, North-Holland, Amsterdam, 1985.
[4] Y. Han, Calderon-type reproducing formula and Tb theorem, Rev. Mat. Iberoamericana, 10 (1994), 51-91.
[5] Y. Han, M.-Y. Lee, and C.-C. Lin, Hardy spaces and the Tb theorem, J. Geom. Anal. 14 (2004), 291-318.
[6] S.-H. Lan, and C.-C. Lin, Weighted Hardy spaces associated to para-accretive functions, Taiwanese J. Math. 14 (2010), no.3B, 1055-1078.
[7] M.-Y. Lee, and C.-C. Lin, Carleson measure spaces associated to para-accretive functions, submitted.
[8] B. Muckenhoupt,Weighted norm inequalities for the Hardy maximal function, Trans. Amer. Math. Soc. 165, (2000), 207-226.
[9] Y. Meyer and R. Coifman, Wavelets. Calderon-Zygmund and Multilinear Operators, Cambridge University Press, Cambridge, 1997.
[10] E. M. Stein and G. Weiss, On the theory of harmonic functions of several variables, Acta. Math. 103 (1960), 25-62.

指導教授

李明憶(Ming-Yi Lee)

審核日期

2011-6-30

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