* Correspondence: [email protected]. cn Department of Mathematics, Harbin Institute of Technology Harbin 150001, P.R.China Full list of author information is available at the end of the article Abstract We establish the Poincaré-type inequalities for the composition of the LaplaceBeltrami operator and the Green’s operator applied to the solutions of the nonhomogeneous A-harmonic equation in the Joh...

Based on the HVZ theorem and dilation analyticity of the pseudorelativistic no-pair Jansen-Hess operator, it is shown that for subcritical potential strength (Z ≤ 90) the singular continuous spectrum is absent. The bound is slightly higher (Z ≤ 102) for the Brown-Ravenhall operator whose eigenvalues λ are, by the virial theorem, confined to λ < 2m if Z ≤ 50.

A singular operator with Cauchy kernel on the subspaces of weight Lebesgue space is considered. A sufficient condition for a bounded action of this operator from a subspace to another subspace of weight Lebesgue space of functions is found. These conditions are not identical withMuckenhoupt conditions. Moreover, the completeness, minimality, and basicity of sines and cosines systems are conside...

1.1 INTRODUCTION This paper gives a survey on additive Schwarz methods applied to the h and p versions of the boundary element method. We consider weakly singular and hypersingular integral equations, namely the single layer potential operator and the normal derivative of the double layer potential operator. That means we have to consider weak formulations of the form

By virtue of Γ−convergence arguments, we investigate the stability of variational eigenvalues associated with a given topological index for the fractional p−Laplacian operator, in the singular limit as the nonlocal operator converges to the p−Laplacian. We also obtain the convergence of the corresponding normalized eigenfunctions in a suitable fractional norm.

We show that the L(w) operator norm of the composition M◦TΩ, where M is the maximal operator and TΩ is a rough homogeneous singular integral with angular part Ω ∈ L∞(Sn−1), depends quadratically on [w]A2 , and this dependence is sharp.

In this paper we study some properties of the classical Arnoldi based methods for solving infinite dimensional linear equations involving compact operators. These problems are intrinsically ill-posed since a compact operator does not admit a bounded inverse. We study the convergence properties and the ability of these algorithms to estimate the dominant singular values of the operator.

Let T be a bounded linear operator on X = (Σ `q)p with 1 ≤ q < ∞ and 1 < p <∞. Then T is a commutator if and only if for all non zero λ ∈ C, the operator T − λI is not X-strictly singular.