内容提要:

(1)  $L^p$空间和插值。[LN-ch1]

(2)  Hardy-Littlewood 极大函数，Fourier变换和分布理论。[LN-ch2,3]

(3)  卷积型奇异积分算子。[LN-ch4,5]

(4)  函数空间和光滑性。[LN-ch6]

(5)  BMO空间和Carleson测度。[LN-ch7]

(6)  非卷积型奇异积分算子。[part of ch4 in【3】]

教材:

（自编讲义，见课程网站内网）.

参考文献:

【1】 E.M. Stein. Singular Integrals and Differentiability Properties of Functions. Princeton Mathematical Series, No. 30. Princeton University Press, Princeton, N.J., 1970.

【2】L. Grafakos. Classical Fourier Analysis, volume 249 of Graduate Texts in Mathematics. Springer, New York, third edition, 2014.

【3】 L. Grafakos. Modern Fourier Analysis, volume 250 of Graduate Texts in Mathematics. Springer, New York, third edition, 2014.

【4】 E.M. Stein and Guido Weiss. Introduction to Fourier Analysis on Euclidean Spaces. Princeton Mathematical Series, No. 32. Princeton University Press, Princeton, N.J., 1971.

【5】 J. Duoandikoetxea. Fourier Analysis, volume 29 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI, 2001. Translated and revised from the 1995 Spanish original by David Cruz-Uribe.

【6】 B.X. Wang, Z.H. Huo, C.C. Hao, and Z.H. Guo. Harmonic Analysis Method for Nonlinear Evolution Equations, volume I. World Scientific Publishing Co. Pte. Ltd., 2011.

【7】周民强, 实变方法 (调和分析讲义)，北京大学出版社.  1999.