JournalsrmiVol. 28, No. 2pp. 351–369

On curvature and the bilinear multiplier problem

  • Sachin Gautam

    Indiana University, Bloomington, USA
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Abstract

We provide sufficient normal curvature conditions on the boundary of a domain DR4D \subset \mathbb{R}^4 to guarantee unboundedness of the bilinear Fourier multiplier operator TD\mathrm{T}_D with symbol χD\chi_D outside the local L2L^2 setting, i.e., from Lp1(R2)×Lp2(R2)Lp3(R2)L^{p_1} ( \mathbb{R}^2) \times L^{p_2} ( \mathbb{R}^2) \rightarrow L^{p_3'} ( \mathbb{R}^2) with 1pj=1\sum \frac{1}{p_j} = 1 and pj<2p_j <2 for some jj. In particular, these curvature conditions are satisfied by any domain DD 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. 351–369

DOI 10.4171/RMI/680