  In this paper, we introduce and study the Fourier transform of functions
which are integrable with respect to a vector measure on a compact group (not
necessarily abelian). We also study the Fourier transform of vector measures.
We also introduce and study the convolution of functions from $L^p$-spaces
associated to a vector measure. We prove some analogues of the classical
Young's inequalities. Similarly, we also study convolution of a scalar measure
and a vector measure.
