IUMJ

Title: Convolution operators defined by singular measures on the motion group

Authors: Luca Brandolini, Giacomo Gigante, Sundaram Thangavelu and Giancarlo Travaglini

Issue: Volume 59 (2010), Issue 6, 1935-1946

Abstract:

This paper contains an $L^p$ improving result for convolution operators defined by singular measures associated to hyper surfaces on the motion group. This needs only mild geometric properties of the surfaces, and it extends earlier results on Radon type transforms on $\mathbb{R}^n$. The proof relies on the harmonic analysis on the motion group.