The boundedness of bilinear Fourier multiplier operators in Besov spaces with variable exponents (Q2043751)

In this paper the author proves boundedness of bilinear Fourier multiplier operator \(T(f,g)\) from \(B^{s(\cdot)}_{p_{1}(\cdot),q(\cdot)}(\mathbb{R}^n) \times B^{s(\cdot)}_{p_{2}(\cdot), q(\cdot)}(\mathbb{R}^n)\) to \(B^{s(\cdot)}_{p(\cdot),q(\cdot)}(\mathbb{R}^n)\) where \(\frac{1}{p_{1}(\cdot)}+\frac{1}{p_{2}(\cdot)}=\frac{1}{p(\cdot)}\) and \(s(\cdot) \in L^{\infty}(\mathbb{R}^n)\) is locally log-Hölder continuous.