### 博碩士論文 952201014 詳細資訊

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(The weighted boundedness of singular integral operators)

 ★ 奇異積分算子的加權模不等式 ★ Marcinkiewicz積分交換子的有界性 ★ 帶變量核之奇異積分算子 ★ 加權赫茲形式哈弟空間上的郝曼德乘算子 ★ 乘積空間上離散型Littlewood-Paley理論 ★ Hardy-Hilbert型式的不等式和Cauchy加法映射的穩定性 ★ 關於section的哈代空間上的分子刻畫 ★ Hardy spaces associated to para-accrective functions ★ 哈地空間在開集合上的極大函數刻畫

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Under the condition related to the Muckenhoupt weights class, we realize that the proof of two weighted norm inequality only depends on one-weighted norm inequality. We give some examples to describe how did we prove it; that is, we proved that the maximal operator , the singular integral operator , the maximal singular integral operator , the Marcinkiewicz integral operator ,the Marcinkiewicz integral operator related to the area integral , and the Marcinkiewicz integral operator related to the Littlewood-Paley -function operator are all bounded from to .
Finally, we prove that the Marcinkiewicz integral operator is bounded from to for another condition of .

★ 有界性
★ 權

★ boundedness
★ singular integral operators

Contents...........................................iii
Introduction.......................................p.2
Definitions and main results.......................p.3
Properties of weights..............................p.6
Proofs of Theorems.................................p.10
References.........................................p.22

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