Endpoint bounds for convolution operators with singular measures

Inequalities for Strongly Singular Convolution Operators

Hölder-Young bounds for operators with regular kernels, Hardy-Littlewood bounds for operators with weakly singular kernels, and Calderon- Zygmund bounds for strongly singular convolution operators over Euclidean space

It easy to see that every bounded linear operator is continuous. It is not hard to show that the converse is also true. The notions of bounded and continuous thereby coincide for linear operators acting between normed spaces. It is customary to prefer the terminology bounded linear operator over that of continuous linear operator. The reason for this preference is the fact that the hard part of...

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 ...

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.

Strong exponent bounds for the local Rankin-Selberg convolution

Let $F$ be a non-Archimedean locally compact field‎. ‎Let $sigma$ and $tau$ be finite-dimensional representations of the Weil-Deligne group of $F$‎. ‎We give strong upper and lower bounds for the Artin and Swan exponents of $sigmaotimestau$ in terms of those of $sigma$ and $tau$‎. ‎We give a different lower bound in terms of $sigmaotimeschecksigma$ and $tauotimeschecktau$‎. ‎Using the Langlands...