Abstract:

We study a class of convolution operators that live at the crossroad of three different areas in singular integrals theory, each interacting with problems in elliptic and parabolic PDEs: our operators have multi-parameter kernels, which are supported along surfaces, and convolution is taken in an homogeneous group that is not Rⁿ (in the Heisenberg group, to be precise). We provide an L² theory for such operators, and show uniformity of the operator norm over a class of surfaces.