Zeitschrift für Analysis und ihre Anwendungen

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Volume 27, Issue 1, 2008, pp. 1–10

DOI: 10.4171/ZAA/1340

Bilinear Estimates Associated to the Schrödinger Equation with a Nonelliptic Principal Part

Eiji Onodera (1)

(1) Mathematical Institute, TOHOKU UNIVERSITY, 980-8578, SENDAI, JAPAN

We discuss bilinear estimates of tempered distributions in the Fourier restriction spaces for the two-dimensional Sch\"odinger equation whose principal part is the d'Alembertian. We prove that the bilinear estimates hold if and only if the tempered distributions are functions.

Keywords: Schrödinger equation, bilinear estimates, local smoothing effect, Strichartz estimate