The endpoint Strichartz estimate
is known to be false by the work of Montgomery-Smith , despite being only "logarithmically far" from being true in some sense. In this short note we show that (in sharp contrast to the Strichartz estimates) the situation is not improved by passing to a bilinear setting; more precisely, if are non-trivial smooth Fourier cutoff multipliers then we show that the bilinear estimate
fails even when , have widely separated supports.
Submitted September 29, 2006. Published December 5, 2006.
Math Subject Classifications: 35J10.
Key Words: Strichartz inequality.
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| Terence Tao |
Department of Mathematics
University of California
Los Angeles, CA 90095-1555, USA
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