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Revista Matemática Iberoamericana

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On curvature and the bilinear multiplier problem

S. Zubin Gautam (1)

(1) Department of Mathematics, Indiana University, Rawles Hall, 831 East 3rd St, IN 47405, BLOOMINGTON, UNITED STATES

We provide sufficient normal curvature conditions on the boundary of a domain $D \subset \mathbb{R}^4$ to guarantee unboundedness of the bilinear Fourier multiplier operator $\mathrm{T}_D$ with symbol $\chi_D$ outside the local $L^2$ setting, i.e., from $L^{p_1} ( \mathbb{R}^2) \times L^{p_2} ( \mathbb{R}^2) \rightarrow L^{p_3'} ( \mathbb{R}^2)$ with $\sum \frac{1}{p_j} = 1$ and $p_j

Keywords: Bilinear Fourier multipliers, multilinear operators