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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/8548完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 沈俊嚴(Chun-Yen Shen) | |
| dc.contributor.author | Yung-Chang Hsu | en |
| dc.contributor.author | 徐永昌 | zh_TW |
| dc.date.accessioned | 2021-05-20T00:57:12Z | - |
| dc.date.available | 2021-02-22 | |
| dc.date.available | 2021-05-20T00:57:12Z | - |
| dc.date.copyright | 2021-02-22 | |
| dc.date.issued | 2021 | |
| dc.date.submitted | 2021-01-26 | |
| dc.identifier.citation | Lennart Carleson. “On convergence and growth of partial sums of Fourier series”. In: Acta Math. 116 (1966), pp. 135–157. doi: 10. 1007/BF02392815. url: https://doi.org/10.1007/BF02392815. Charles Fefferman. “Pointwise Convergence of Fourier Series”. In: Annals of Mathematics 98.3 (1973), pp. 551–571. issn: 0003486X. url: http://www.jstor.org/stable/1970917. Michael Lacey and Christoph Thiele. “Lp Estimates on the Bilinear Hilbert Transform for 2 < p < ∞”. In: Annals of Mathematics 146.3 (1997), pp. 693–724. issn: 0003486X. url: http://www.jstor.org/ stable/2952458. Michael Lacey and Christoph Thiele. “A proof of boundedness of the Carleson operator”. In: Mathematical Research Letters 7 (July 2000), pp. 361–370. doi: 10.4310/MRL.2000.v7.n4.a1. J. Duoandikoetxea et al. Fourier Analysis. American Mathematical Society, 2001. isbn: 9780821821725. url: https://books.google. com.tw/books?id=6fgRCgAAQBAJ. Elias M. Stein and Stephen Wainger. “Oscillatory integrals related to Carleson’s theorem”. In: Mathematical Research Letters 8.6 (2001), pp. 789–800. doi: 10.4310/mrl.2001.v8.n6.a9. url: https: //doi.org/10.4310%2Fmrl.2001.v8.n6.a9. Victor Lie. The (weak-L2) Boundedness of The Quadratic Carleson Operator. 2008. arXiv: 0710.2168 [math.CA]. Michael Bateman and Christoph Thiele. “Lp estimates for the Hilbert transforms along a one-variable vector field”. In: Analysis PDE 6.7 (Dec. 2013), pp. 1577–1600. issn: 2157-5045. doi: 10.2140/ apde.2013.6.1577. url: http://dx.doi.org/10.2140/apde. 2013.6.1577. Andrei K. Lerner and Fedor Nazarov. Intuitive dyadic calculus: the basics. 2015. arXiv: 1508.05639 [math.CA]. Pavel Zorin-Kranich. Modulation invariant operators. 2019. arXiv: 1902.10577 [math.CA]. Victor Lie. “The Polynomial Carleson operator”. In: Annals of Math- ematics 192.1 (2020), pp. 47–163. issn: 0003486X, 19398980. url: https://www.jstor.org/stable/10.4007/annals.2020.192.1. 2. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/8548 | - |
| dc.description.abstract | 本文針對多項式卡爾松算子高維推廣在勒貝格空間下的有界性作深入探討。相比於Victor Lie與Pavel Zorin-Kranich之前的工作，該文章的主要貢獻包含：以具體的構造法來確認細節論證、用稀疏算子的語言來重新詮釋部分證明、及提供一個具教學啟發性的完整說明。 | zh_TW |
| dc.description.abstract | We deeply study the Lp boundedness of the generalization of Polynomial Carleson Operator. Our main contributions, comparing to previous works done by Victor Lie and by Pavel Zorin-Kranich, are to verify de- tails with explicit constructions, modify some part with language of Sparse Dominance, and provide a heuristic interpretation about the whole treatment in general. | en |
| dc.description.provenance | Made available in DSpace on 2021-05-20T00:57:12Z (GMT). No. of bitstreams: 1 U0001-2501202116313700.pdf: 1045869 bytes, checksum: 7a6b49b8c5f3667f7c8e1c6da112eaa7 (MD5) Previous issue date: 2021 | en |
| dc.description.tableofcontents | 1 Introduction 2 1.1 BasicNotions............................. 3 1.2 Motivation .............................. 5 1.3 MainResult.............................. 8 2 Mathematical Jigsaw Puzzle 10 2.1 Cut out the Pieces .......................... 10 2.2 Find Good Configurations...................... 11 2.3 Combinatorial Wizardry and Analytic Magecraft . . . . . . . . . 12 3 Tools and Facts 13 3.1 Local Oscillation of Polynomial................... 13 3.2 Van der Corput Estimate ...................... 14 3.3 Sparse Language and Ambient System............... 15 3.4 Modified Settings........................... 16 4 Decomposition of the Operator 19 4.1 Reduction and Linearization..................... 19 4.2 Tile Decomposition and Trivial Estimate. . . . . . . . . . . . . . 20 4.3 Adaptive Christ Grid Construction................. 22 5 From Incidental Geometry to Order Theory and Combinatorics 24 5.1 Conversion and Basic Operations.................. 24 5.2 Geometric and Analytic Interaction................. 26 5.3 Feffermann’s Trick .......................... 30 5.4 Boundary Removal.......................... 36 5.5 Separation Upgrade ......................... 38 6 Search for Good Trades 39 6.1 Trade-off: Polynomial v.s. Exponential............... 39 6.2 Charles Fefferman’s Exceptional Set ................ 42 6.3 Victor Lie’s Stopping Collection................... 43 6.4 PavelZorin-Kranich’s Modifications ................ 46 6.5 Explicit Construction of Smooth Carpet . . . . . . . . . . . . . . 50 7 Sparse Domination of Sparse Parts 53 7.1 Reductions .............................. 53 7.2 Sparse Dominance .......................... 58 7.3 Density Extraction.......................... 60 8 TT* - T*T Arguments for Cluster Parts 64 8.1 Reductions .............................. 64 8.2 Pointwise Control on Cluster .................... 67 8.3 Extraction of Separation Factor................... 73 8.4 Support Restriction and Cross-Level Decay . . . . . . . . . . . . 78 8.5 Row Configuration .......................... 80 8.6 Almost Orthogonality ........................ 82 8.7 Bateman’s Extrapolation Argument ................ 84 References 93 | |
| dc.language.iso | en | |
| dc.title | 多項式調變不變奇異積分算子 | zh_TW |
| dc.title | Polynomial Modulation Invariant Singular Integral Operator | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 109-1 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 王振男(Jenn-Nan Wang),黃啟瑞(Chii-Ruey Hwang) | |
| dc.subject.keyword | 時頻分析,多重解析度分析,CZ算子,稀疏壓制,TT*-T*T方法, | zh_TW |
| dc.subject.keyword | Time-Frequency Analysis,Multi-Resolution Analysis,CZO,Sparse Dominance,TT* method, | en |
| dc.relation.page | 93 | |
| dc.identifier.doi | 10.6342/NTU202100160 | |
| dc.rights.note | 同意授權(全球公開) | |
| dc.date.accepted | 2021-01-27 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
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