On some singular convolution operators

Singular Convolution Operators on the Heisenberg Group

1. Statement of results and outline of method. The purpose of this note is to announce results dealing with convolution operators on the Heisenberg group. As opposed to the well-known situation where the kernels are homogeneous and C°° away from the origin, the kernels we study are homogeneous but have singularities on a hyperplane. Convolution operators with such kernels arise in the study of ...

Inequalities for Strongly Singular Convolution Operators

Strongly Singular Convolution Operators on the Heisenberg Group

We consider the L mapping properties of a model class of strongly singular integral operators on the Heisenberg group H; these are convolution operators on H whose kernels are too singular at the origin to be of Calderón-Zygmund type. This strong singularity is compensated for by introducing a suitably large oscillation. Our results are obtained by utilizing the group Fourier transform and unif...

A Note on Calderón-zygmund Singular Integral Convolution Operators

Convolution Calderón-Zygmund singular integral operators with rough kernels

A survey of known results in the theory of convolution type Calderón-Zygmund singular integral operators with rough kernels is given. Some recent progress is discussed. A list of remaining open questions is presented.