Tohoku Mathematical Journal
2014
March
SECOND SERIES VOL. 66, NO. 1

Tohoku Math. J.
66 (2014), 55-76

Title BOUNDEDNESS CRITERION FOR BILINEAR FOURIER MULTIPLIER OPERATORS

Author Akihiko Miyachi and Naohito Tomita

(Received February 18, 2013)
Abstract. Bilinear Fourier multiplier operators corresponding to multipliers that are singular at the origin are considered. New criterions on such multipliers to assure the boundedness of the corresponding operators from $L^p \times L^q$ to $L^r$, $1/p+1/q=1/r$, are given in the range $1<p,q \le \infty$, $2/3<r<\infty$.

Mathematics Subject Classification. Primary 42B15; Secondary 42B20.
Key words and phrases. Bilinear Fourier multipliers, Hörmander multiplier theorem, Littlewood-Paley theory.

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