On curvature and the bilinear multiplier problem (Q427926)

The paper deals with some bilinear analogues of the celebrated ball multiplier problem. Contrary to the linear setting, the bilinear one is not well-understood even if some ideas developed by \textit{C. Fefferman} in [Ann. Math. (2) 94, 330--336 (1971; Zbl 0234.42009)] can be adapted. However, the author gives sufficient normal curvature conditions on \(\partial D\) to obtain unboundedness (outside the local \(L^2\) setting) of the bilinear Fourier multiplier operator with the characteristic function of the domain \(D\subset \mathbb R^4\) as symbol.