In this paper we characterize the boundedness on the product of Sobolev spaces Hs() × Hs() on the unit circle , of the bilinear form Λb with symbol b ∈ Hs() given by $${{\Lambda}_b} (\varphi, \psi): = \int_{\open T} {\left({{{(- {\Delta })}^s} + I} \right)(\varphi \psi)(\eta)b(\eta) {\rm d}\sigma (\eta).}$$