Bilinear oscillatory integrals and boundedness for new bilinear multipliers

Bilinear Fourier integral operator and its boundedness

We consider the bilinear Fourier integral operatorS(f, g)(x) =ZRdZRdei1(x,)ei2(x,)(x, , ) ˆ f()ˆg()d d,on modulation spaces. Our aim is to indicate this operator is well defined onS(Rd) and shall show the relationship between the bilinear operator and BFIO onmodulation spaces.

Bilinear multipliers and transference

(defined for Schwarzt test functions f and g in ) extends to a bounded bilinear operator from Lp1 (R)×Lp2 (R) into Lp3 (R). The theory of these multipliers has been tremendously developed after the results proved by Lacey and Thiele (see [16, 18, 17]) which establish that m(ξ,ν) = sign(ξ +αν) is a (p1, p2)-multiplier for each triple (p1, p2, p3) such that 1 < p1, p2 ≤∞, p3 > 2/3, and each α∈R \...

A homomorphism theorem for bilinear multipliers

In this paper we prove an abstract homomorphism theorem for bilinear multipliers in the setting of locally compact Abelian (LCA) groups. We also provide some applications. In particular, we obtain a bilinear abstract version of K. de Leeuw’s theorem for bilinear multipliers of strong and weak type. We also obtain necessary conditions on bilinear multipliers on non-compact LCA groups, yielding b...

Bilinear Identity for q - Hypergeometric Integrals

Boundedness of bilinear operators with nonsmooth symbols

We announce the Lp-boundedness of general bilinear operators associated to a symbol or multiplier which need not be smooth. We establish a general result for multipliers that are allowed to have singularities along the edges of a cone as well as possibly at its vertex. It thus unifies ealier results of CoifmanMeyer for smooth multipliers and ones, such the Bilinear Hilbert transform of Lacey-Th...