局部平均分解以及最佳加權上界

Chun-Bao Hsu; 許竣堡

請用此 Handle URI 來引用此文件： http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/73101

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	Chun-Bao Hsu	en
dc.contributor.author	許竣堡	zh_TW
dc.date.accessioned	2021-06-17T07:17:33Z	-
dc.date.available	2019-07-17
dc.date.copyright	2019-07-17
dc.date.issued	2019
dc.date.submitted	2019-07-11
dc.identifier.citation	[1] A. Lerner A simple proof of the A 2 conjecture, Internat. Math. Res. Notices, 2013. [2] David Cruz-Uribe, Sfo, José María Martell, and Carlos Pérez Sharp weighted estimates for approximating dyadic operators, Electron. Res. An- nounc. Math. Sci. Preprint,arXiv:1001.4724, 2010. [3] Oliver Dragicević, Loukas Grafakos, María Cristina Pereyra, and Stefanie Petermichl Extropolation and sharp norm estimates for classical operators on weighted Lebesgue spaces, Publ. Mat., 49(1):73–91, 2005. [4] T.P. Hytönen The sharp weighted bound for general Calderón-Zygmund operator, Annals of Math, 2012. [5] Sandra Pott, Maria Carmen Reguera, Eric T. Sawyer, and Brett D. Wick The linear bound for the natural weighted resolution of the Haar shift, 2013. [6] T.P. Hytönen The sharp weighted bound for general Calderón-Zygmund operator, Annals of Math, 2012.
dc.identifier.uri	http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/73101	-
dc.description.abstract	本篇論文主要是研究奇異積分算子的最佳加權上界問題，而此問題相當於研究奇異積分算子在 L2 加權的有界性，而本篇主要介紹的手法是 A. Lerner 在 2013 發表論文中所使用的局部平均分解。藉由對於函數跟函數局部中位數的誤差估計，可被局部平均震盪函數的組合以及 dyadic local sharp maximal function 所控制，且他們分別又可以被控制，進而得到我們的結論。同時我們也會介紹 D. Cruz-Uribe,J.Martell,C.Pérez 他們的一篇文章，使用局部加權來處理 Haar shift operator 的最佳加權上界問題。	zh_TW
dc.description.abstract	In this paper,we mainly study the sharp A2 bound of singular integral operators, and this problem is equivalent to study the L2 weighted bound of the singular integral operators. The main method introduced in this thesis is the local mean decomposition invented by A.Lerner in his 2013 paper. All the estimates can be controlled by the combination of the local mean oscillation and the dyadic local sharp maximal function,and they can be respectively controlled. In addition, we will also introduce the work of D.Cruz-Uribe, J.Martell, C.Pérez, in which the sharp weighted bound of Haar shift operators are studied.	en
dc.description.provenance	Made available in DSpace on 2021-06-17T07:17:33Z (GMT). No. of bitstreams: 1 ntu-108-R05221003-1.pdf: 527752 bytes, checksum: f61cad65629eb8f2c96685702909abc5 (MD5) Previous issue date: 2019	en
dc.description.tableofcontents	1 Introduction 5 2 Calderón-Zygmund operator 6 3 Weighted Inequalities 10 4 Local Mean Oscillation 12 5 Estimate to Sharp A 2 bound 31 6 Haar shift operator and sharp A 2 bound 48 7 Open Problem 54 8 Reference 55
dc.language.iso	zh-TW
dc.subject	奇異積分算子	zh_TW
dc.subject	哈爾算子	zh_TW
dc.subject	局部平均分解	zh_TW
dc.subject	最佳加權上界	zh_TW
dc.subject	local mean decomposition	en
dc.subject	Calderon-Zygmund operator	en
dc.subject	sparse dyadic cubes	en
dc.subject	sharp A2 bound	en
dc.subject	Harr shift operator	en
dc.title	局部平均分解以及最佳加權上界	zh_TW
dc.title	Local mean decomposition and Sharp A2 bound	en
dc.type	Thesis
dc.date.schoolyear	107-2
dc.description.degree	碩士
dc.contributor.oralexamcommittee	陳逸昆(I-Kun Chen),林欽誠(Chin-Cheng Lin),司靈得(Daniel Eli Spector)
dc.subject.keyword	奇異積分算子,最佳加權上界,局部平均分解,哈爾算子,	zh_TW
dc.subject.keyword	Calderon-Zygmund operator,local mean decomposition,sparse dyadic cubes,sharp A2 bound,Harr shift operator,	en
dc.relation.page	55
dc.identifier.doi	10.6342/NTU201901396
dc.rights.note	有償授權
dc.date.accepted	2019-07-11
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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