We provide sufficient normal curvature conditions on the boundary of a domain to guarantee unboundedness of the bilinear Fourier multiplier operator with symbol outside the local setting, i.e., from with and for some . In particular, these curvature conditions are satisfied by any domain that is locally strictly convex at a single boundary point.
Cite this article
Sachin Gautam, On curvature and the bilinear multiplier problem. Rev. Mat. Iberoam. 28 (2012), no. 2, pp. 351–369DOI 10.4171/RMI/680