On curvature and the bilinear multiplier problem

2009/07/24 by S. Zubin Gautam, Gautam, S. Zubin
Mathematics · #Advanced Harmonic Analysis Research #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.0907.4216

Abstract

We provide sufficient normal curvature conditions on the boundary of a domain D ⊂ \BBR⁴ to guarantee unboundedness of the bilinear Fourier multiplier operator \T_D with symbol χ_D outside the local L² setting, i.e. from L^p₁ (\BBR²) × L^p₂ (\BBR²) → L^p₃' (\BBR²) with ∑ (1)/(p_j) = 1 and p_j <2 for some j. In particular, these curvature conditions are satisfied by any domain D that is locally strictly convex at a single boundary point.

Citations

• The Multiplier Problem for the Ball

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