NOTES ON THE SPACES OF BILINEAR MULTIPLIERS

A locally integrable function m(xi, eta) defined on R-n x R-n is said to be a bilinear multiplier on R-n of type (p(1), p(2), p(3)) if B-m(f, g)(x) = integral(Rn) integral(Rn) (f) over cap(xi)(g) over cap(eta)m(xi, eta)e(2 pi i <xi+eta,x >) d xi d eta defines a bounded bilinear operator from L-p1(R-n) x L-p2 (R-n) to L-p3 (R-n). The study of the basic properties of such spaces is investigated and several methods of constructing examples of bilinear multipliers are provided. The special case where m(xi,eta) = M(xi - eta) for a given M defined on R-n is also addressed.