In this paper we continue our investigations of square function inequalities in harmonic analysis. Here we investigate oscillation and variation inequalities for singular integral operators in dimensions d ≥ 1. Our estimates give quantitative information on the speed of convergence of truncations of a singular integral operator, including upcrossing and λ jump inequalities.

In [21] this theorem is used by L. v. Wolfersdorf to consider singular integral equations on the real halfline involving the singular (complex) Hilbert operator. This theory is extended by Askabarov in [1] to the complex case. We want to investigate a special family of singular integral operators in Clifford analysis which has in IR an application to the nonlinear magnetic field equation ([5]) ...

In this article the problem of solving a system of singular nonlinear equations will be discussed. New the iterative 2-order method for this problem is presented. The article includes the numerical results for the method. 1. Problem Let : n n F D R R ⊂ → be a nonlinear operator, D is an open set. The point 0 x D ∈ is given. The problem of solving a system of nonlinear equations consists in find...

The aim of this paper is to address computational aspects of the total energy singular vector analysis of atmospheric chemical transport models. We discuss the symmetry of the tangent-linear/adjoint operator for stiff systems. Results for a 3D simulation with real data reveal that the total energy singular vectors depend on the target domain, simulation window, chemical reactions, and meteorolo...

By virtue of an operator-theoretical approach, we deal with hyperbolic singular perturbation problems for integrodifferential equations. New convergence theorems for such singular perturbation problems are obtained, which generalize some previous results by This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, an...

V. D. Milman proved in [14] that the product of two strictly singular operators on L p [0, 1] (1 p < ∞) or on C[0, 1] is compact. In this note we utilize Schreier families S ξ in order to define the class of S ξ-strictly singular operators, and then we refine the technique of Milman to show that certain products of operators from this class are compact, under the assumption that the underlying ...

By fixed point theorem of a mixed monotone operator, we study boundary value problems to nonlinear singular fourth-order differential equations, and provide sufficient conditions for the existence and uniqueness of positive solution. The nonlinear term in the differential equation may be singular.

We establish sharp L2-Sobolev estimates for classes of pseudodifferential operators with singular symbols [27, 20] whose non-pseudodifferential (Fourier integral operator) parts exhibit two-sided fold singularities. The operators considered include both singular integral operators along curves in R2 with simple inflection points and normal operators arising in linearized seismic imaging in the ...

An elementary lemma is used in order to show that the natural inclusion Jp → Jq of James spaces is superstrictly singular for p < q. As a consequence, it is shown that an operator without nontrivial invariant subspaces constructed by Charles Read is superstrictly singular.

A recent novel derivation of the representation of Virasoro singular vectors in terms of Jack polynomials is extended to the supersymmetric case. The resulting expression of a generic super-Virasoro singular vector is given in terms of a simple di erential operator (whose form is characteristic of the sector, Neveu-Schwarz or Ramond) acting on a Jack superpolynomial. The latter is indexed by a ...