  A known Hardy-Littlewood theorem asserts that if both the function and its
conjugate are of bounded variation, then their Fourier series are absolutely
convergent. It is proved in the paper that the same result holds true for
functions on the whole axis and their Fourier transforms with certain
adjustments. The proof of the original Hardy-Littlewood theorem is derived from
the obtained assertion. It turned out that the former is a partial case of the
latter when the function is supposed to be of compact support. A similar result
as the obtained one but for radial functions is derived from the
one-dimensional case.
