Lu Sh., Ding Y., Yan D. Singular Integrals and Related Topics

Singapore: World Scientific Publishing. – 2007. – 280 p. It is well-known that singular integrals are continuously regarded as a central role in harmonic analysis. There are many nice books related to singular integrals. In this book, there are at least two sides which differ from the other books. One of them is to establish more perfect theory of singular integrals. It includes not only the case of smooth kernels, but also the case of rough kernels. In the same way, we deal with some related operators, such as fractional integral operators and Littlewood-Paley operators. The other is to introduce more new theory on some oscillatory singular integrals with polynomial phases. This book is mainly provided to graduate students in analysis field. However, it is also beneficial to researchers in mathematics. This book consists of five chapters. Chapter 1 is devoted to the theory of the Hardy-Littlewood maximal operator as the basis of singular integrals and other related operators. It also includes the basic theory of the Ap weights. Chapter 2 is related to the theory of singular integrals. Chapter 3 is devoted to fractional integrals. In the same way, we will pay more attention to the case of rough kernels. It includes not only the A(p, q) weight theory of fractional integrals with rough kernels, but also the theory of its commutators. Chapter 4 is to introduce a class of oscillatory singular integrals with polynomial phases. Chapter 5 is related to the Littlewood-Paley theory.Hardy-Littlewood Maximal Operator.
Singular Integral Operators.
Fractional Integral Operators.
Oscillatory Singular Integrals.
Littlewood-Paley Operator.