The Bilinear Multiplier Problem for Strictly Convex Compact Sets
نویسندگان
چکیده
We study the question whether characteristic functions of strictly convex compact sets with smooth boundaries in R are L × L → L bounded bilinear Fourier multiplier operators on R × R. When n ≥ 2 we answer this question in the negative outside the local L case, i.e., when 1/p + 1/q = 1/r and 2 ≤ p, q, r′ <∞ fails. Our proof is based on a suitable adaptation of the Kakeya type construction employed by Fefferman in the solution of the multiplier problem for the ball on L(R) for p 6= 2.
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