Multilinear singular operators with fractional rank

Multilinear Singular Operators with Fractional Rank

We prove bounds for multilinear operators on R given by multipliers which are singular along a k dimensional subspace. The new case of interest is when the rank k/d is not an integer. Connections with the concept of true complexity from Additive Combinatorics are also investigated.

Multilinear Singular Integral Operators with Variable Coefficients

Some recent results for bilinear or multilinear singular integrals operators are presented. The focus is on some of the results that can be viewed as natural counterparts of classical theorems in Calderón-Zygmund theory, adding to the already existing extensive literature in the subject. In particular, two different classes of operators that can be seen as bilinear counterparts of linear Calder...

Operators with Singular Continuous Spectrum: Ii. Rank One Operators

For an operator, A, with cyclic vector φ, we study A+ λP where P is the rank one projection onto multiples of φ. If [α,β] ⊂ spec(A) and A has no a.c. spectrum, we prove that A + λP has purely singular continuous spectrum on (α, β) for a dense Gδ of λ’s. §

Some Estimates for Rough Multilinear Fractional Integral Operators and Rough Multi-sublinear Fractional Maximal Operators

It is well known that, for the purpose of researching non-smoothness partial differential equation, mathematicians pay more attention to the singular integrals with rough kernel. Moreover, the fractional type operators and their weighted boundedness theory play important roles in harmonic analysis and other fields, and the multilinear operators arise in numerous situations involving product-lik...

Estimates of Multilinear Singular Integral Operators and Mean Oscillation