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4.1
80 reviews受傅里叶级数与积分的研究启发,本书引进了诸如Hardy-Littlewood极大函数和Hilbert变换这些经典论题,全书的其余部分则致力于研讨奇异积分算子和乘子,讨论了该理论的经典内容和近期发展,诸如加权不等式、H¹、BMO空间以及T1定理。
第一章回顾了傅里叶级数与积分;第二章和第三章介绍了此领域的两个基本算子:Hardy-Littlewood极大函数和Hilbert变换。第四章和第五章讨论了奇异积分,包括其现代推广。第六章研讨了H¹、BMO和奇异积分间的突系;第七章讲述了加权范数不等式,第八章讨论了Littlewood-Paley理论,它的发展激发了大量应用。最后一章以一个重要结果即T1定理结尾,它在此领域具有关键性的作用。
本书是1995年西班牙文版的更新和翻译版本。书的核心部分只做了少量改动,但是在每章的“注释和进一步的结果”小节中有着相当大的扩充并吸收了新的论题、结果和参考文献。本书适合希望找到一本关于奇异算子和乘子的经典理论简明教材的研究生阅读,预备知识包括勒贝格积分和泛函分析的基本知识。