| DC 欄位 |
值 |
語言 |
| DC.contributor | 數學系 | zh_TW |
| DC.creator | 古文仁 | zh_TW |
| DC.creator | Wen-Jen Ku | en_US |
| dc.date.accessioned | 2016-6-15T07:39:07Z | |
| dc.date.available | 2016-6-15T07:39:07Z | |
| dc.date.issued | 2016 | |
| dc.identifier.uri | http://ir.lib.ncu.edu.tw:88/thesis/view_etd.asp?URN=102221019 | |
| dc.contributor.department | 數學系 | zh_TW |
| DC.description | 國立中央大學 | zh_TW |
| DC.description | National Central University | en_US |
| dc.description.abstract | 在此篇論文裡，我們先探究在不同函數空間上的傅立葉轉換，例如說在L^1空間、在L^p空間1 < p ≤ 2及在Schwartz空間。接下來，我們會利用一些性質和定理去探究Hardy-Littlewood的極大函數，並證明其有weak (1,1)和strong(p,p)＂ 1 < p≤∞＂ 的性質。最後，我們將探討奇異積分算子的有界性，我們將專注在Hilbert transform。 | zh_TW |
| dc.description.abstract | In this thesis, we study various properties of Fourier transform. We first study the Fourier transform on Schwartz classes, and extend to L^p spaces for 1 ≤p≤2. Secondly, we shall focus on the Hardy-Littlewood maximal function, and prove that it is weak (1, 1) and strong(p, p) ＂for 1 < p≤∞＂ . At the end, we will discuss one of the most important singular intergrals, the so-called Hilbert transform. | en_US |
| DC.subject | 傅利葉級數 | zh_TW |
| DC.subject | 歐氏空間 | zh_TW |
| DC.subject | 施瓦茨空间 | zh_TW |
| DC.subject | 哈代－李特爾伍德極大函數 | zh_TW |
| DC.subject | 奇異積分算子 | zh_TW |
| DC.subject | 希爾伯特轉換 | zh_TW |
| DC.title | 歐氏空間富式分析的探討 | zh_TW |
| dc.language.iso | zh-TW | zh-TW |
| DC.title | A study of Fourier series in Euclidean spaces | en_US |
| DC.type | 博碩士論文 | zh_TW |
| DC.type | thesis | en_US |
| DC.publisher | National Central University | en_US |