Lecture 4: Multiparameter Convolution Type Singular Integrals

In this lecture we study the corresponding behavior of Calderon-Zygmund operators in the two parameter setting. We will see that we need to incorporate more complicated conditions on the kernel so that we can obtain the desired estimates. Here, we will just focus on the case of $L^2$ since the case of general p requires more technology than we have at the moment. The idea will be to show that the kernel in question has a bounded Fourier transform and then we can deduce the resulting $L^2$ boundedness easily.