On the boundedness of bilinear operators on products of Besov and Lebesgue spaces

We prove mapping properties of the form and , for certain related indices p₁,p₂,p₃,q₁,q₂,α₁,α₂∈R, where T is a bilinear Hörmander-Mihlin multiplier or a molecular paraproduct. Applications to bilinear Littlewood-Paley theory are discussed.     

Weighted Norm Inequalities for Paraproducts and Bilinear Pseudodifferential Operators with Mild Regularity

We establish boundedness properties on products of weighted Lebesgue, Hardy, and amalgam spaces of certain paraproducts and bilinear pseudodifferential operators with mild regularity. We do so by showing that these operators can be realized as generalized bilinear Calderón–Zygmund operators.      

Multipliers between Sobolev spaces and fractional differentiation

We characterize the pointwise multipliers which maps a Sobolev space to a Sobolev space in the case |s|<r<d/2.