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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 |
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系所名稱 Department |
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畢業學年期 Year, semester |
語文別 Language |
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學位類別 Degree |
頁數 Number of pages |
31 |
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研究生 Author |
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指導教授 Advisor |
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召集委員 Convenor |
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口試委員 Advisory Committee |
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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 |
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統計 Statistics |
本論文已被瀏覽 5719 次,被下載 2227 次 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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