專任教師
李明憶 的照片
教授兼系主任

李明憶

研究領域

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學歷

國立中央大學博士

經歷

  1. 2019/01~2022/12  科技部自然科學及永續研究發展司數學學門複審委員會委員
  2. 2015/08 ~   中央大學數學系 教授
  3. 2010/08 ~ 2015/07 中央大學數學系 副教授
  4. 2007/02 ~ 2010/07 中央大學數學系 助理教授
  5. 2004/01 ~ 2007/01 中研院數學研究所 博士後研究

榮譽

  1. 國立中央大學113年度「特聘教授」
  2. 國立中央大學112年度「學術研究傑出獎」
  3. 國立中央大學110年度「學術研究傑出獎」
  4. 國立中央大學109年度「學術研究傑出獎」
  5. 國立中央大學102學年度「教學優良獎」
  6. 國家理論科學中心2008年「年輕理論學者獎」
  7. 國立中央大學95學年度「新聘傑出教師獎勵」
     

著作

  1. Boundedness of Dunkl–Riesz transforms on Dunkl–Besov spaces, (with Chin-Cheng Lin and Keng Hao Ooi), Illinois J. Math. (68) (2024) 755–779.
  2. Algebra of Calderón-Zygmund operators on product spaces. Ann. Math. Sci. Apple. 9 (2024), no 3, 701–749.
  3. The two weight inequality for the Poisson semigroup on manifold with ends, (with Xuan Thinh Duong, Ji Li and Brett D. Wick), Communication in Analysis and Geometry, 32(2024), 1339-1374.
  4. Riesz transforms and commutators in the Dunkl setting, (with Yongsheng Han, Ji Li and Brett D. Wick), Anal. Math. Phys. 14 (2024) no. 3,  Paper No. 46.
  5. Hardy spaces associated to self-adjoint operators on general domains, (with Xuan Thinh Duong, Ji Li and Chin-Cheng Lin), Collect. Math. 75(2024), 305-330.
  6. Hardy spaces on open subsets of Rn, (with Chin-Cheng Lin and Keng Hao Ooi), Journal of Geometric Analysis 34(2024), no. 1, Paper No. 20, 38 pp.
  7. Lipschitz and Triebel–Lizorkin spaces, commutators in Dunkl setting, (with Yongsheng Han,Ji Li and Brett D. Wick ), Nonlinear Analysis 237 (2023), Paper No. 113365, 36 pp.
  8. A Study of One-Sided Singular Integral and Function Space via Reproducing Formula, (with Zunwei Fu, Xianming Hou and Ji Li), Journal of Geometric Analysis 33(2023), no. 9, Paper No. 289, 34 pp
  9. Maximal function, Littlewood--Paley theory, Riesz transform and atomic decomposition in the multi-parameter flag setting, (with Yongsheng Han,Ji Li and Brett D. Wick),  Mem. Amer. Math. Soc. 279(2022) no 1373.
  10. Monge-Ampere singular integral operators acting on Triebel-Lizorkin spaces, (with Meifang Cheng, Chin-Cheng Lin and Meng Qu), Appl. Anal. 100(2021), 923-963.
  11. Besov and Hölder spaces on spaces of homogeneous type, (with Yongshen Han and Chin-Cheng Lin), Studia Mathematica 255 (2020) , 219-263.
  12. Boundedness of Monge-Ampere singular integral operators on Besov spaces, (with Yongshen Han and Chin-Cheng Lin), Appl. Anal. 99(2020), 1910-1938.
  13. Product Hardy spaces associated with para-accretive functions and Tb theorem, (with Ji Li and Chin-Cheng Lin), New York J. Math. 25(2019), 1438-1483.
  14. Hardy spaces associated with Monge-Ampere equation, (with Yongshen Han and Chin-Cheng Lin), Journal of Geometric Analysis, 28(2018), 3312-3347.
  15. Carleson measure characterization of weighted BMO associated with a family of general sets, (with Yong Ding and Chin-Cheng Lin), Journal of Geometric Analysis, 27(2017), 842-867.
  16. On weak-star convergence in product Hardy spaces on spaces of homogeneous type, (with Ji Li and Lesley A. Ward), Studia Math. 235(2016), 251-267.
  17. Tb theorem on product spaces, (with Yongsheng Han and Chin-Cheng Lin), Mathematical Proceedings Cambridge Philosophical Society 161(2016), 117-141.
  18. Characterization of Campanato spaces associated with parabolic sections, (with Chin-Cheng Lin and Xinfeng Wu), Asian Journal of Mathematics, 20(2016), no 1, 183-198.
  19. VMO Space associated with parabolic sections and its application, (with Ming-Hsiu Hsu), Canadian Mathematical Bulletin 58(2015), no. 3, 507-518.
  20. Boundedness of Calderon-Zygmund operators on weighted product Hardy spaces, Journal of operator theory, 72 (2014), 101-119.
  21. Ap,E weights, maximal operators, and Hardy spaces associated with a family of general sets, (with Yong Ding and Chin-Cheng Lin), The Journal of Fourier Analysis and Application, 20 (2014), 608-667.
  22. Calderon-Zygmund operators on weighted Hardy spaces, Potential Analysis, 38 (2013), 699-709.
  23. Boundedness of Riesz transforms on weighted Carleson measure spaces, Studia Math., 209 (2012), 169-187.
  24. The boundedness of Monge-Ampere singular integral operators, The Journal of Fourier Analysis and Application, 18 (2012), 211-222.
  25. Carleson measure spaces associated to para-accretive functions (with Chin-Cheng Lin), Communications in Contemporary Mathematics, vol. 14, no.1, Article. ID 1250002, 19 pages, 2012, doi: 10.1142/S0219199712500022.
  26. The boundedness of Calderon-Zygmund operators by wavelet characterization, (with Cheng-Cong Hung), Acta Mathematica Sinica, English series, 28 (2012), no. 6, 1237-1248.
  27. Fractional integral operators on weighted anisotropic Hardy spaces, (with Sen-Hua Lan and Chin-Cheng Lin), Journal of operator theory, 68(2012), 3-17.
  28. Atomic decomposition and boundedness of operators on weighted Hardy spaces, (with Yongsheng Han and Chin-Cheng Lin), Canadian Mathematical Bulletin, 55 (2012), no. 2, 303-314.
  29. Para-accretive functions and Hardy spaces, (with Yongsheng Han and Chin-Cheng Lin), Integral Equations and Operator Theory, 72 (2012), 67-90.
  30. H pw  boundedness of Calderon-Zygmund type operators, Communication in Mathematical Analysis, 9 (2010), no. 1, 77-83.
  31. The continuity of pseudo-differential operators on weighted local Hardy spaces, (with Chin-Cheng Lin and Ying-Chieh Lin), Studia Math. 198 (2010), 69-77.
  32. Calderon-Zygmund operators on product Hardy spaces, (with Han Yongsheng , Chin-Cheng Lin and Ying-Chien Lin), Journal of Functional Analysis, 258 (2010), 2834-2861.
  33. A wavelet characterization for the dual of weighted Hardy spaces, (with Chin-Cheng Lin and Ying-Chien Lin), Proceeding of the American Mathematical Society, 137(2009), 4219-4225.
  34. Boundedness of singular integral operators with variable kernels, (with Chin-Cheng Lin, Ying-Chien Lin and Dunyan Yan), Journal of Mathematical Analysis and Applications, 348(2008), 787-796.
  35. Generalized Calderon-Zygmund operators on homogeneous groups and applications (with Der-Chen Chang), Applicable Analysis, 87(2008), 531-554.
  36. Large-time behavior of solutions for the Boltzmann equation with hard potentials (with Tai-Ping Liu and Shin-Hsien Yu), Communications in Mathematical Physics, 269 (2007) 17-37.
  37. Weighted norm inequality of Bochner-Riesz means, Journal of Mathematical Analysis and Applications, 324 (2006) 1274-1281.
  38. Banach algebra of Calderon-Zygmund operators associated to para-accretive functions (with Yongsheng Han and Chin-Cheng Lin), The journal of Fourier Analysis and Applications, 12 (2006), 581-596.
  39. Hormander multipliers for weighted Herz-type Hardy spaces (with Chin-Cheng Lin and Yu-Tien Lin), Acta Mathematica Sinica, English series 22 (2006) 1509-1518.
  40. Convolution operators on the weighted Herz-type Hardy spaces, Journal of Approximation theory, 138 (2006) 197-210.
  41. H pw boundedness of Riesz transforms, Journal of Mathematical Analysis and Applications (with Chin-Cheng Lin and Wei-Chi Yang), 301 (2005), 394-400.
  42. Weighted L p boundedness of Marcinkiewicz integral (with Chin-Cheng Lin), Integral Equations and Operator Theory, 49 (2004), 211-220.
  43. Hardy spaces and the Tb theorem (with Yongsheng Han and Chin-Cheng Lin), Journal of Geometric Analysis, 14 (2004), 291-318.
  44. Marcinkiewicz integral on weighted Hardy spaces (with Yong Ding and Chin-Cheng Lin), Archiv der Mathematik, 80 (2003), 620-629.
  45. Fractional integrals on weighted Hardy spaces (with Yong Ding and Chin-Cheng Lin), Journal of Mathematical Analysis and Applications, 282 (2003), 356-368.
  46. The molecular characterization of weighted Hardy spaces (with Chin-Cheng Lin), Journal of Functional Analysis, 188 (2002), 442-460.

研究領域

富氏分析Fourier Analysis

灰色粗線是方波：x < 0 時為 −1，x > 0 時為 1。三條曲線逼近它：S₁ 是一條正弦波；S₃ 較接近方波但仍有起伏；S₁₅ 幾乎貼合方波，但在 x = 0 與 ±π 的跳躍處兩側各有一個明顯的尖峰，最高約 1.18。
方波 f(x) = sgn(sin x) 的富氏級數部分和 Sₙ(x) = (4/π) Σₖ₌₁ⁿ sin((2k − 1)x)/(2k − 1)，n = 1、3、15。部分和在 f 的連續點收斂到 f，但在跳躍點附近恆有約為跳躍量 9% 的過衝（Gibbs 現象）：n → ∞ 時最大值趨近 (2/π)Si(π) ≈ 1.179。

富氏分析（Fourier analysis）研究如何把函數分解為正弦、餘弦等簡單振盪的疊加。Fourier 在 1807 年研究熱傳導時提出以三角級數表示函數；週期函數的富氏級數與非週期函數的富氏轉換是此領域的兩個基本工具，其推廣稱為調和分析（harmonic analysis）。

核心課題包括富氏級數與富氏轉換的收斂性與可和性、Plancherel 定理、Lᵖ 空間上的有界算子（如 Hilbert 轉換與奇異積分算子）、極大函數，以及局部緊群上的調和分析。富氏方法是研究偏微分方程、數論與機率論的重要工具，也是訊號處理、影像壓縮與量子力學的數學基礎。

數學主題分類（MSC2020）：42（Harmonic analysis on Euclidean spaces）、43（Abstract harmonic analysis）