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In this paper we prove the Convolution Theorem for the Fourier Integral transform over a subset of bounded variation functions which vanish at infinity. This subset is dense in L2(R) . Moreover, it does not have inclusion relations with the space of Lebesgue integrable functions. We employ the Henstock-Kurzweil integral. Mathematics subject classification (2010): 42A38, 42A85; 26A39, 26A45.

On the convolution theorem for the Fourier transform of BV_0 functions