請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/80334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 | Chong-Wei Liang | en |
| dc.contributor.author | 梁崇瑋 | zh_TW |
| dc.date.accessioned | 2022-11-24T03:04:40Z | - |
| dc.date.available | 2021-07-23 | |
| dc.date.available | 2022-11-24T03:04:40Z | - |
| dc.date.copyright | 2021-07-23 | |
| dc.date.issued | 2021 | |
| dc.date.submitted | 2021-06-26 | |
| dc.identifier.citation | C. Fefferman and E. M. Stein. “Some Maximal Inequalities”. In: American Journal of Mathematics 93.1 (1971), pp. 107–115. issn: 00029327, 10806377. url: http://www.jstor.org/stable/2373450. SAGUN CHANILLO and RICHARD L. WHEEDEN. “Some Weighted Norm Inequalities for the Area Integral”. In: Indiana University Mathematics Journal 36.2 (1987), pp. 277–294. issn: 00222518, 19435258. url: http://www.jstor.org/stable/24894300. Stephen M. Buckley. “Estimates for Operator Norms on Weighted Spaces and Reverse Jensen Inequalities”. In: Transactions of the American Mathematical Society 340.1 (1993), pp. 253–272. issn: 00029947. url: http://www.jstor.org/stable/2154555. C. Pérez. “Weighted Norm Inequalities for Singular Integral Operators”. In: Journal of the London Mathematical Society 49.2 (Apr. 1994), pp. 296–308. issn: 0024-6107. doi: 10.1112/jlms/49.2.296. eprint: https://academic.oup.com/jlms/article-pdf/49/2/296/2712599/49-2-296.pdf. url: https://doi.org/10.1112/jlms/49.2.296. David Cruz-Uribe and C. Neugebauer. “The Structure of the Reverse Hölder Classes”. In: Transactions of the American Mathematical Society 347 (Aug. 1995). doi: 10.2307/2154763. J. Duoandikoetxea et al. Fourier Analysis. American Mathematical Society, 2001. isbn: 9780821821725. url: https://books.google.com.tw/books?id=6fgRCgAAQBAJ. María J. Carro et al. “Maximal Functions and the Control of Weighted Inequalities for the Fractional Integral Operator”. In: Indiana University Mathematics Journal 54.3 (2005), pp. 627–644. issn: 00222518, 19435258. url: http://www.jstor.org/stable/24902292. Maria Carmen Reguera and Christoph Thiele. The Hilbert transform does not map L1(Mw) to L1,∞(w). 2010. arXiv: 1011.1767 [math.CA]. Maria Carmen Reguera. “On Muckenhoupt–Wheeden Conjecture”. In: Advances in Mathematics 227.4 (2011), pp. 1436–1450. issn: 0001-8708. doi: https://doi.org/10.1016/j.aim.2011.03.009. url: https://www.sciencedirect.com/science/article/pii/S0001870811000946. Andrei K. Lerner. A simple proof of the A2 conjecture. 2012. arXiv: 1202.2824 [math.CA]. José M. Conde-Alonso and Guillermo Rey. “A pointwise estimate for positive dyadic shifts and some applications”. In: Mathematische Annalen 365.3-4 (Oct. 2015), pp. 1111–1135. issn: 1432-1807. doi:10.1007/s00208-015-1320-y. url: http://dx.doi.org/10.1007/s00208-015-1320-y. Carlos Domingo-Salazar, Michael Lacey, and Guillermo Rey. “Borderline weak-type estimates for singular integrals and square functions”. In: Bulletin of the London Mathematical Society 48.1 (Dec. 2015), pp. 63–73. issn: 1469-2120. doi: 10.1112/blms/bdv090. url: http://dx.doi.org/10.1112/blms/bdv090. Tuomas Hytönen and Carlos P´erez. The L(log L) endpoint estimate for maximal singular integral operators. 2015. arXiv: 1503.04008 [math.CA]. Andrei K. Lerner and Fedor Nazarov. Intuitive dyadic calculus: the basics. 2015. arXiv: 1508.05639 [math.CA]. Cong Hoang and Kabe Moen. Muckenhoupt-Wheeden conjectures for sparse operators. 2017. arXiv: 1609.03889 [math.CA]. Andrei K. Lerner and Sheldy Ombrosi. Some remarks on the pointwise sparse domination. 2019. arXiv: 1901.00195 [math.CA]. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/80334 | - |
| dc.description.abstract | "我們這篇論文，主要是研究奇異積分算子與分數次積分算子的弱有界性。對於一個正則稀疏算子 ，任何權重 w，此正則稀疏算子 會把 L^1(M_\alpha(M_{L\log_2 L(\log_3 L)^\delta})w) 這個空間映射到 L^{1,\infty}(w)，其中 \delta>1。而我們的主定理是建立在 Perez ， Lacey 還有 Hytönen 這幾位數學家的工作之上，我們直接找出哪一類的楊式函數會使得正則稀疏算子將 L^1(M_\alpha(M_\phi )w) 映射到 L^{1,\infty}(w) 這個空間。" | zh_TW |
| dc.description.provenance | Made available in DSpace on 2022-11-24T03:04:40Z (GMT). No. of bitstreams: 1 U0001-2106202116430100.pdf: 2049968 bytes, checksum: 8b8ae44f9db670f3e55a6497dd9e1856 (MD5) Previous issue date: 2021 | en |
| dc.description.tableofcontents | 1.Introduction 1 1.1 Motivations 1 1.2 Main Results 4 1.3 General Notations 5 2.Weighted and Dyadic Theorem 7 2.1 The A_p Condition and Its Structure 10 2.2 Strong-Type Inequalities with Weights 13 2.3 A_1 Weights and Some Characterizations 18 2.4 Weighted Inequalities for Singular Integrals 20 2.5 Dyadic Theorem 25 3.The Structure of Reverse Hölder Class 28 3.1 Basic Setting and Preliminary Result 28 3.2 Two Weight Version of Reverse Hölder Inequality 31 3.3 The Minimal Operator 34 3.4 The Class RH_infinity 37 3.5 Application to RH_s Class 40 3.6 The Structure of A_1 and RH_\infinity 45 4.Logarithmic Maximal Functions 48 4.1 Orlicz Space 49 4.2 General Maximal Operator 52 4.3 A_1 Charaterization for General Maximal Operator 54 5.Endpoint Estimate for Maximal Singular Integral Operator 58 5.1 Concise Logarithm Scale Control for M.V.C 59 5.2 Rubio de Francia Algorithm 62 5.3 Proof of Theorem 5.1.2 64 5.4 Proof of Theorem 5.1.1 66 6. M.W.C for Fractional Integral Operator 70 6.1 The Counterexamples of M.W.C 72 6.2 Perez's Modification 75 6.3 Local and Global Part: Radial Weight 80 7.Iterated Logarithm Technique 85 7.1 Elementary Lemma 87 7.2 Core Technique : Layer Decomposition 87 7.3 Suitable Logarithm Function 90 8.M.W.C for Sparse Operators 92 8.1 Construction of Tricky Weight 94 8.2 Control of The Maximal Function 96 9.Improvement of Fractional M.W.C 102 9.1 Statement and Proof of The Main Result 102 References 107 | |
| dc.language.iso | en | |
| dc.subject | 稀疏控制 | zh_TW |
| dc.subject | 穆肯霍普特-威登猜想 | zh_TW |
| dc.subject | 卡爾德隆-齊格蒙德算子 | zh_TW |
| dc.subject | 分數次積分算子 | zh_TW |
| dc.subject | Sparse Dominance | en |
| dc.subject | Muckenhoupt-Wheeden Conjecture | en |
| dc.subject | Calderon-Zygmund Operator | en |
| dc.subject | Fractional Integral Operator | en |
| dc.title | 奇異積分算子與分數次積分算子的弱邊界估計 | zh_TW |
| dc.title | Borderline Weak Type Estimates for Singular Integral Operators and Fractional Integral Operators | en |
| dc.date.schoolyear | 109-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | #VALUE! | |
| dc.subject.keyword | 穆肯霍普特-威登猜想,卡爾德隆-齊格蒙德算子,分數次積分算子,稀疏控制, | zh_TW |
| dc.subject.keyword | Muckenhoupt-Wheeden Conjecture,Calderon-Zygmund Operator,Fractional Integral Operator,Sparse Dominance, | en |
| dc.relation.page | 109 | |
| dc.identifier.doi | 10.6342/NTU202101083 | |
| dc.rights.note | 同意授權(限校園內公開) | |
| dc.date.accepted | 2021-06-28 | |
| 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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