On some bilinear problems on weighted Hardy‐Sobolev spaces

In this paper we study the bilinear problem of characterizing the positive Borel measures μ on S n , satisfying\documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty} $$ \left|\int _{{\bf S}^n}f \overline{g }\,d\mu \right|\le C\Vert f\Vert _{H_s^2(w)}\Vert g\Vert _{H_t^2(w)}, $$ \end{document} where \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$H_s^2(w)$\end{document} and \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$H_t^2(w)$\end{document} are weighted Hardy‐Sobolev spaces, under adequate conditions on the weight w .