On curvature and the bilinear multiplier problem
نویسندگان
چکیده
We provide sufficient normal curvature conditions on the boundary of a domain D ⊂ R to guarantee unboundedness of the bilinear Fourier multiplier operator TD with symbol χD outside the local L 2 setting, i.e. from L1 (R) × L2 (R) → L ′ 3 (R) with P 1 pj = 1 and pj < 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.
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