Bulletin of the
Korean Mathematical Society BKMS

Let T be a bilinear Calder\'{o}n-Zygmund operator, b\in \cup_{q>1}L_{loc}^{q}(G). We firstly obtain a constructive proof of the weak factorisation of Hardy spaces, then we establish the characterization of BMO spaces by the boundedness of the commutator [b, T]_{j} in variable Lebesgue spaces.

Keywords: bilinear Calder\'{o}n-Zygmund operators； variable Lebesgue spaces； stratified groups

MSC numbers: 42B20； 42B35； 43A80