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 note, it is proved that the Marcinkiewicz integral with rough kernel defined by

Let h(y) be a bounded radial function and Ω (y ′) an H 1 function on the unit sphere satisfying the cancelation condition. Then the Marcinkiewicz integral operator µ Ω related to the Littlewood-Paley g−function is defined by µ Ω (f)(x) = ∞ 0 |F t (x)| 2 dt t 3 1 2 , (1) where F t (x) = |x−y|≤t Ω (x − y) |x − y| d−1 h (|x − y|) f (y)dy (2) and h(y) ∈ L ∞ (R +). In this paper, we prove that the o...

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...

We prove the properties of induced conjugacy classes, without using the original proof by Lusztig and Spaltenstein in the unipotent case, by adapting Borho’s simpler arguments for induced adjoint orbits. We study properties of equivariant fibrations of prehomogeneous affine spaces, especially the existence of relative invariants. We also detect prehomogeneous affine spaces as subquotients of ca...

In this contribution we define a new class of non-linear integrals based on decomposition integrals. These integrals are motivated by greediness of many real-life situations. Another view on this new class of integrals is that it is a generalization of both the Shilkret and PAN integrals. Moreover, it can be seen as an iterated Shilkret integral. Also, an example in time-series analysis is prov...

The classical Black–Scholes hedging strategy of a European contingent claim may require rapid changes in the replicating portfolio. One approach to avoid this is to impose a priori bounds on the variations of the allowed trading strategies, called gamma constraints. Under such a restriction, it is in general no longer possible to replicate a European contingent claim, and super-replication is a...

Ten years ago A. Zorich discovered, by computer experiments on interval exchange transformations, some striking new power laws for the ergodic integrals of generic non-exact Hamiltonian flows on higher genus surfaces. In Zorich’s later work and in a joint paper authored by M. Kontsevich, Zorich and Kontsevich were able to explain conjecturally most of Zorich’s discoveries by relating them to th...