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博碩士論文 etd-0618106-215033 詳細資訊
Title page for etd-0618106-215033
論文名稱
Title
哈弟不等式在加權哈弟空間上的研究
A study of Hardy's inequalities in the weighted Hardy spaces
系所名稱
Department
畢業學年期
Year, semester
語文別
Language
學位類別
Degree
頁數
Number of pages
31
研究生
Author
指導教授
Advisor
召集委員
Convenor
口試委員
Advisory Committee
口試日期
Date of Exam
2006-06-16
繳交日期
Date of Submission
2006-06-18
關鍵字
Keywords
加權、哈弟
Hardy, atom, weighted, Hermite
統計
Statistics
本論文已被瀏覽 5719 次,被下載 2227
The thesis/dissertation has been browsed 5719 times, has been downloaded 2227 times.
中文摘要
在這篇論文,我們證明了weighted atom 有關於Hermite expansions 的不等式。但我們想要把這個不等式套用在一維的加權哈弟空間上,也一樣能得到相同形式的不等式。
Abstract
In this paper, we prove a weighted atom inequality for Hermite expansions and want to obtain similar type of inequalities for 1-dimensional Hermite expansions of weighted Hardy's inequalities.
目次 Table of Contents
1 Introduction 2
2 Preliminaries 4
2.1 The atomic characterization of Hp(Rn)
2.2 The atomic characterization of Hpw(Rn)
2.3 Hermiteexpansions
3 The main result 15
參考文獻 References
[1] P. L. Duren, Theory of Hp Spaces, Academic Press, N. Y., (1971).
[2] A. Zygmund, Trigonometric Series, Cambridge Univ. Press, (1959).
[3] L. Colzani and G. Travaglini, Hardy-Lorentz spaces and expansions in eigenfunctions of the Laplace-Beltrami operator on compact manifolds, Colloq. Math. 58 (1990), 305-316. MR 92c:58142.
[4] Y. Kanjin, Hardy’s inequalities for Hermite and Laguerre expansions, Bull. London Math. Soc. 29 (1997), 331-337. MR 98f:42024
[5] M. Statake, Hardy’s inequalities for Laguerre expansions, J. Math. Soc. Japan 52 (2000), 17-24. Mr 2001c:42014
[6] S. THANGAVELU, Lectures on Hermite and Laguerre expansions, Mathematical Notes, 42, Princetion Univ.Press, (1993).
[7] R. RADHA, Hardy type inequalities, Taiwanese J. Math., 4 (2000), 447-456.
[8] R. RADHA and S. THANGAVELU, Hardy’s inequalities for Hermite and Laguerre expansions, Proc. Amer. Math. Soc., 132 (12) (2004) 3525-3536.
[9] C. Fe erman and E. M. Stein, Hp spaces of several variables, Acta Math. 129 (1972), 137-193.
[10] R.R.Coifman, A real variable characterization of Hp, Studia Math. 51 (1974), 269-274.
[11] R.H.Latter, A characterization of Hp(Rn) in terms of atoms, Studia Math. 62 (1978), 93-101.
[12] J. Garcia-Cuerva, Weighted Hp spaces, Dissertations Math. 162 (1979), 1-63.
[13] J.-O. Str¨omberg and A. Torchinsky, ”Weighted Hardy Spaces,” Lecture Notes in Mathematics, Vol. 1381, Spring-Verlag, Berlin/New York, (1989).
[14] B. Muckenhoupt, Weighted norm inequalities for the Hardy mximal funcions, Trans. Amer. Math. Soc. 165 (1972), 207-226.
[15] R. Hunt, B. Muckenhoupt, and R. Wheeden, Weighted norm inequalities for the conjugate for the conjugate function and Hilbert transform, Trans. Amer. Math. Soc. 176 (1973), 227-251.
[16] R. R. Coifman and C. Fe erman, Weighted norm inequalities for maximal functions and singular integrals, Studia Math. 51 (1974), 241-250.
[17] E. M. Stein, ”Singular Integrals and Di erentiability Properties of Functions,”
Princeton Univ. Press, Princeton, NJ, (1970).
[18] S. THANGAVELU, Lectures on Hermite and Laguerre expansions, Mathematical Notes, 42, Princeton Univ. Press, (1993).
[19] R. BALASUBRAMANIAN AND R. RADHA, Hardy-type inequalities for Hermite expansions, JIPAM 6(1), Article 12, (2005).
[20] GUO BEN-YU, Error estimation of Hermite spectral method for nonlinear partial di erential equations, Math. comp.,V.68, 227 (1999), 1067-1078.
[21] Ming-Yi Lee and Chin-Cheng Lin, The molecular characterization of weighted Hardy spaces, J. Funct. Anal. 188 (2002), 442-460.
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