Multiparameter singular integrals and maximal functions (Q1203380)

We prove \(L^ p\)-boundedness for a class of singular integral operators and maximal operators associated with a general \(k\)-parameter family of dilations on \(\mathbb{R}^ n\). This class includes homogeneous operators defined by kernels supported on homogeneous manifolds. For singular integrals, only certain ``minimal'' cancellation is required of the kernels, depending on the given set of dilations.