We study the strongly singular volume integral operator that describes the scattering of time-harmonic electromagnetic waves. For the case of piecewise constant material coefficients and smooth interfaces, we determine the essential spectrum. We show that it is a finite set and that the operator is Fredholm of index zero in H(curl) if and only if the relative permeability and permittivity are b...

a method for solving a class of weakly singular volterra integral equations is given by using the fractional differential transform method. the approximate solution of these equa­tions is calculated in the form of a finite series with easily computable terms. while in some examples this series solution increased up to the exact closed solution, in some other examples, we can see the accuracy an...

Let T be the Calderón-Zygmund singular integral operator, a well-known result of Coifman et al. (see [6]) states that the commutator [b,T]( f ) = T(b f )− bT( f ) (where b ∈ BMO) is bounded on Lp(Rn) (1 < p <∞); Chanillo (see [1]) proves a similar result when T is replaced by the fractional integral operator; in [8, 9], these results on the TriebelLizorkin spaces and the case b ∈ Lipβ (where Li...

Let T be the singular integral operator, a well-known result of Coifman, Rochberg and Weiss [6] which states that the commutator [b,T ] = T (b f )− bT f (where b ∈ BMO) is bounded on Lp(Rn)(1 < p < ∞). Chanillo [1] proves a similar result when T is replaced by the fractional integral operator. In [9,11], these results on the Triebel–Lizorkin spaces and the case b∈Lipβ (where Lipβ is the homogen...

We consider a left-linear analogue to the classical Riemann problem: Dau = 0 in Rn\Γ u+ = H(x)u− + h(x) on Γ |u(x)| = O(|x|n2−1) as |x| → ∞. For this purpose, we state a Borel-Pompeiu formula for the disturbed Dirac operator Da = D+a with a paravector a and some functiontheoretical results. We reformulate the Riemann problem as an integral equation: Pau+ HQau = h on Γ, where Pa = 2(I + Sa) and ...

in this paper, using a generalized translation operator, we prove theestimates for the generalized fourier-bessel transform in the space l2 on certainclasses of functions.

On the Hilbert space ̃L2(T) the singular integral operator with non-Carleman shift and conjugation K = P+ + (aI + AC)P− is considered, where P± are the Cauchy projectors, A = m ∑ j=0 ajU j , a,aj , j = 1,m , are continuous functions on the unit circle T , U is the shift operator and C is the operator of complex conjugation. Some estimates for the dimension of the kernel of the operator K are obt...

Must the Fourier series of an L function converge pointwise almost everywhere? In the 1960’s, Carleson answered this question in the affirmative, by studying a particular type of maximal singular integral operator, which has since become known as a Carleson operator. In the past 40 years, a number of important results have been proved for generalizations of the original Carleson operator. In th...

in this paper‎, ‎we consider a general integral operator $g_n(z).$ the main object of the present paper is to study some properties of this integral operator on the classes $mathcal{s}^{*}(alpha),$ $mathcal{k}(alpha),$ $mathcal{m}(beta),$ $mathcal{n}(beta)$ and $mathcal{kd}(mu,beta).$‎

In this paper we consider a class of weighted integral operators on L2(0,∞) and show that they are unitarily equivalent to little Hankel operators between weighted Bergman spaces of the right half plane. We use two parameters α, β ∈ (−1,∞) and involve two weights to define Bergman spaces of the domain and range of the little Hankel operators. We obtained conditions for the Hankel integral opera...