We provide sufficient normal curvature conditions on the boundary of a domain D ⊂ R to guarantee unboundedness of the bilinear Fourier multiplier operator TD with symbol χD outside the local L 2 setting, i.e. from L1 (R) × L2 (R) → L ′ 3 (R) with P 1 pj = 1 and pj < 2 for some j. In particular, these curvature conditions are satisfied by any domain D that is locally strictly convex at a single ...

Let b be aBMO-function. It is well-known that the linear commutator [b, T ] of a Calderón-Zygmund operator T does not, in general, map continuously H(R) into L(R). However, Pérez showed that if H(R) is replaced by a suitable atomic subspace H b(R ) then the commutator is continuous from H b(R ) into L(R). In this paper, we find the largest subspace H b (R ) such that all commutators of Calderón...

There are two parts for this paper. In the first part, we extend some results in a recent paper by Du, Guth, Li and Zhang to more general class of phase functions. The main methods Bourgain-Demeter's $l^2$ decoupling theorem induction on scales. second prove positive maximal extension operator hypersurfaces with principal curvatures. sharp $L^2$ estimates Du Zhang, bilinear method Wolff Tao.

This is a short review of the Kadomtsev–Petviashvili hierarchies types $$\mathrm{B}$$ and $$\mathrm{C}$$ . The main objects are $$L$$ operator, wave auxiliary linear problems for function, bilinear identity tau function. All them discussed in paper. Connections with usual (type- $$\mathrm{A}$$ ) hierarchy clarified. Examples soliton solutions dispersionless limit also considered.

The paper considers representing bilinear forms by linear operators in the case of a Krull valuation. More precisely, after making some suitable assumptions, we prove that if φ is a non-degenerate bilinear form, then φ is representable by a unique linear operator A whose adjoint operator A∗ exists.

The notion of vertex operator coalgebra is presented which corresponds to the family of correlation functions modeling one string propagating in space-time splitting into n strings in conformal field theory. This notion is in some sense dual to the notion of vertex operator algebra. We prove that any vertex operator algebra equipped with a non-degenerate, Virasoro preserving, bilinear form give...

We present a general result of approximate controllability for the bilinear Schrödinger equation (with wave function varying in the unit sphere of an infinite dimensional Hilbert space), under the hypothesis that the Schrödinger operator has discrete spectrum and that the control potential couples all eigenstates. The control method is based on a tracking procedure for the Galerkin approximatio...