In this paper, the authors establish the sharp maximal estimates for the multilinear iterated commutators generated by [Formula: see text] functions and multilinear singular integral operators with generalized kernels. As applications, the boundedness of this kind of multilinear iterated commutators on the product of weighted Lebesgue spaces and the product of variable exponent Lebesgue spaces ...

We consider the Multilinear set S defined as the set of binary points (x, y) satisfying a collection of multilinear equations of the form yI = ∏ i∈I xi, I ∈ I, where I denotes a family of subsets of {1, . . . , n} of cardinality at least two. Such sets appear in factorable reformulations of many types of nonconvex optimization problems, including binary polynomial optimization. A great simplifi...

Multilinear interpolation is a powerful tool used in obtaining strong type boundedness for a variety of operators assuming only a finite set of restricted weak-type estimates. A typical situation occurs when one knows that a multilinear operator satisfies a weak L estimate for a single index q (which may be less than one) and that all the adjoints of the multilinear operator are of similar natu...

I t1 1 ⊗ · · · ⊗ tn n γ. This problem will be called the weak multilinear Hausdorff problem of moments for μk. Comparison with classical results will allow us to relate the weak multilinear Hausdorff problem with the multivariate Hausdorff problem. A solution to the strong multilinear Hausdorff problem of moments will be provided by exhibiting necessary and sufficient conditions for the existen...

In this paper we obtain new inclusion and coincidence theorems for absolutely or multiple summing multilinear mappings. In particular, we derive optimal coincidence theorems of Bohnenblust-Hille type for multilinear forms on K-convex Banach spaces of cotype 2.

The conditions under which, multilinear forms (the symmetric case and the non symmetric case),can be written as a product of linear forms, are considered. Also we generalize a result due to S.Kurepa for 2n-functionals in a group G.

The Whitney module of a matroid is a natural analogue of the tensor algebra of the exterior algebra of a vector space that takes into account the dependencies of the matroid. In this paper we indicate the role that tableaux can play in describing the Whitney module. We will use our results to describe a basis of the Whitney module of a certain class of matroids known as freedom (also known as S...

Abstract. In this work we investigate the construction of Carleson measures from families of multilinear integral operators applied to tuples of L∞ and BMO functions. We show that if the family Rt of multilinear operators possesses cancellation in each variable, then for BMO functions b1, . . . , bm, the measure |Rt(b1, . . . , bm)(x)|dxdt/t is Carleson. However, if the family of multilinear op...