Title: Algebras of SIOs with kernels controlled by multiple norms
Abstract: We study algebras of singular integral operators on nilpotent Lie groups that arise when one considers the composition of Calderon-Zygmund operators with different homogeneities. The operators in these algebras are characterized in several different ways: in terms of size and cancellation conditions of the kernel, in terms of the size of the Fourier transform, and in terms of decompositions into dyadic sums of bump functions. The operators are pseudo-local and bounded on $L^p$ for $1<p<\infty$. This is a report on joint work with Fulvio Ricci, Elias M. Stein, and Stephen Wainger.