陆善镇编著的《奇异积分和相关论题》是一部为分析专业的研究生量身定做的入门书籍。本书以欧几里得空间为背景，清晰明确地阐释了奇异积分及其相关话题。后三章有大量作者在调和分析方面做出的科研成果和继续研究所需要的背景材料。

本书的读者对象包括数学专业高年级本科生和科研人员。

preface

1 hardy-littlewood maximal operator

 1.1 hardy-littlewood maximal operator

 1.2 calderdn-zygmund decomposition

 1.3 marcinkiewicz interpolation theorem

 1.4 weighted norm inequalities

 1.5 notes and references

2 singular integral operators

 2.1 calderon-zygmund singular integral operators

 2.2 singular integral operators with homogeneous kernels

 2.3 singular integral operators with rough kernels

 2.4 commutators of singular integral operators

 2.5 notes and references

3 fractional integral operators

 3.1 riesz potential

 3.2 weighted boundedness of riesz potential

 3.3 fractional integral operator with homogeneous kernels

 3.4 weighted boundedness of tω,a

 3.5 commutators of riesz potential

 3.6 commutators of fractional integrals with rough kernels

 3.7 notes and references

4 oscillatory singular integrals

 4.1 oscillatory singular integrals with homogeneous smooth kernels

 4.2 oscillatory singular integrals with rough kernels

 4.3 oscillatory singular integrals with standard kernels

 4.4 multilinear oscillatory singular integrals with rough kernels

 4.5 multilinear oscillatory singular integrals with standard kernels

 4.6 notes and references

5 littlewood-paley operator

 5.1 littlewood-paley g function

 5.2 weighted littlewood-paley theory

 5.3 littlewood-paley g function with rough kernel

 5.4 notes and references

bibliography

index