Banach algebra of the Fourier multipliers on weighted Banach function spaces

Let M-X,(w)(R) denote the algebra of the Fourier multipliers on a separable weighted Banach function space X(R, w). We prove that if the Cauchy singular integral operator S is bounded on X( R, w), then M-X,M-w( R) is continuously embedded into L-infinity(R). An important consequence of the continuous embedding M-X,M-w(R) subset of L-infinity(R) is that M-X,M-w(R) is a Banach algebra.