Convolution operators defined by singular measures on the motion group Luca BrandoliniGiacomo GiganteSundaram ThangaveluGiancarlo Travaglini Primary 43A80Secondary 42B1044A12. radon transform$L^p$ improvingMotion Group 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. Indiana University Mathematics Journal 2010 text pdf 10.1512/iumj.2010.59.4100 10.1512/iumj.2010.59.4100 en Indiana Univ. Math. J. 59 (2010) 1935 - 1946 state-of-the-art mathematics http://iumj.org/access/