In this paper an algorithm is presented for the regularization of singular integrals with any degrees of singularity, which may be employed in all three-dimensional problems analyzed by Boundary Elements. The integrals in Boundary Integrals Equations are inherently singular. For example, one can mention the integrals confronted in potential problems to evaluate the flow or the gradient of the f...

In this paper, we establish CBMO estimates for the multilinear commutator related to the Marcinkiewicz operator in Herz and Morrey-Herz spaces.

All equivalence classes for electromagnetic potentials and space-time metrics of Stackel spaces provided that Hamilton–Jacobi equation Klein–Gordon–Fock a charged test particle can be integrated by the method complete separation variables are found. The is carried out using sets mutually commuting integrals motion type (1.1) whereby in privileged coordinate system, given equations turn into par...

We consider a class of Hamiltonian systems in 3 degrees freedom, with particular type quadratic integral and which includes the rational Calogero-Moser system as case. For general class, we introduce separation coordinates to find separable (and therefore Liouville integrable) system, two integrals. This gives coupling large potentials, generalising series potentials are parabolic coordinates. ...

The fair price of a financial option on an asset that follows a Poisson jump diffusion process satisfies a partial integro-differential equation. When numerical methods are used to solve such equations the integrals are usually evaluated using either quadrature methods or fast Fourier methods. Quadrature methods are expensive since the integrals must be evaluated at every point of the mesh. Tho...

We study the Marcinkiewicz integral operator M f(x) = ( ∫∞ −∞ | ∫ |y|≤2t f (x − (y))(Ω(y)/|y|n−1)dy|2dt/22t)1/2, where is a polynomial mapping from Rn into Rd and Ω is a homogeneous function of degree zero on Rn with mean value zero over the unit sphere Sn−1. We prove an Lp boundedness result of M for rough Ω. 2000 Mathematics Subject Classification. 42B20, 42B15, 42B25.

Marcinkiewicz multipliers are L bounded for 1 < p < ∞ on the Heisenberg group H ≃ C × R (D. Muller, F. Ricci and E. M. Stein [25], [26]). This is surprising in that this class of multipliers is invariant under a two parameter group of dilations on C × R, while there is no two parameter group of automorphic dilations on H. This lack of automorphic dilations underlies the inability of classical o...

We investigate the relationships between the Marcinkiewicz-Zygmund-type inequalities and certain shifted average operators. Applications to the mean boundedness of a quasi-interpolatory operator in the case of trigonometric polynomials, Jacobi polynomials, and Freud polynomials are presented.