In this paper we use the Morse theory of the Yang-Mills-Higgs functional on the singular space of Higgs bundles on Riemann surfaces to compute the equivariant cohomology of the space of semistable U(2, 1) and SU(2, 1) Higgs bundles with fixed Toledo invariant. In the non-coprime case this gives new results about the topology of the U(2, 1) and SU(2, 1) character varieties of surface groups. The...

As the development of singular integral operators, their commutators have been well studied(see [1][3-5][10-12]). Let T be the Calderón-Zygmund singular integral operator. A classical result of Coifman, Rocherberg and Weiss (see [3]) state that commutator [b, T ](f) = T (bf) − bT (f)(where b ∈ BMO(Rn)) is bounded on Lp(Rn) for 1 < p < ∞. In [10-12], the sharp estimates for some multilinear comm...

The time evolution operator K is introduced in the graded context and its main properties are discussed. In particular, the operator K is used to analize the projectability of constraint functions arising in the Lagrangian formalism for singular Lagrangians.

In this paper, we investigate the singular solutions of time harmonic Maxwell equations in a domain which has edges and polyhedral corners. It is now well known that in the presence of non-convex edges, the solution elds have no square inte-grable gradients in general and that the main singularities are the gradients of singular functions of the Laplace operator. We show how this type of result...

An example is given of a strictly singular non-compact operator on a Hereditarily Indecomposable, reflexive, asymptotic `1 Banach space. The construction of this operator relies on the existence of transfinite c0-spreading models in the dual of the space.

In this work, we continue the study of precise functional properties of a linear operator linked with Boltzmann quadratic operator, started in Part I. This is done for singular cross-sections. In particular, we show Calderon-Zygmund type estimates.

We consider a singular Sturm-Liouville differential expression with an indefinite weight function and we show that the corresponding self-adjoint differential operator in a Krein space locally has the same spectral properties as a definitizable operator.

We show that many invariant subspaces M for d-shifts (S1, . . . , Sd) of finite rank have the property that the orthogonal projection PM onto M satisfies PMSk − SkPM ∈ L, 1 ≤ k ≤ d for every p > 2d, L denoting the Schatten-von Neumann class of all compact operators having p-summable singular value lists. In such cases, the d tuple of operators T̄ = (T1, . . . , Td) obtained by compressing (S1, ....