Bilinear Multipliers of Small Lebesgue spaces

Lebesgue Spaces for Bilinear Vector Integration Theory

In this note we shall announce results concerning the structure of £^0^)> the space of 2s-valued functions integrable with respect to a measure m:H->L(E, F), where L(E,F) is the class of bounded operators from the Banach space E into the Banach space F. The bilinear integration theory introduced here is more restrictive than the one developed by Bartle [1], but it is general enough to allow a n...

Notes on the Spaces of Bilinear Multipliers

A locally integrable function m(ξ, η) defined on R × R is said to be a bilinear multiplier on R of type (p1, p2, p3) if Bm(f, g)(x) = Z

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 \...

Decomposition of Lebesgue Spaces

On the boundedness of bilinear operators on products of Besov and Lebesgue spaces

We prove mapping properties of the form T : Ḃ11 p1 × L p2 → Ḃ22 p3 and T : Ḃ11 p1 × Ḃ α2,q2 p2 → L p3 , for certain related indices p1, p2, p3, q1, q2, α1, α2 ∈ R, where T is a bilinear Hörmander-Mihlin multiplier or a molecular paraproduct. Applications to bilinear Littlewood-Paley theory are discussed.