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

Convolution operators defined by singular measures on the motion group