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 $mathcal{KD}(mu,beta).$‎

The Gaussian scale-space is a singular integral convolution operator with scaled Gaussian kernel. For a large class of singular integral convolution operators with differentiable kernels, a general method for constructing mother wavelets for continuous wavelet transforms is developed, and Calderón type inversion formulas, in both integral and semi-discrete forms, are derived for functions in L ...

We construct smooth asymptotically AdS5×S solutions of Type IIB supergravity corresponding to all the half-BPS surface operators in N = 4 SYM. All the parameters labeling a half-BPS surface operator are identified in the corresponding bubbling geometry. We use the supergravity description of surface operators to study the action of the SL(2, Z) duality group of N = 4 SYM on the parameters of th...

We give the Jordan form and the Singular Value Decomposition for an integral operator N with a non-symmetric kernel N(y, z). This is used to give solutions of Fredholm equations for non-symmetric kernels, and to determine the behaviour of N n and (NN ∗)n for large n.

We prove optimal bounds in L2(R2) for the maximal operator obtained by taking a singular integral along N arbitrary directions in the plane. We also give a new proof for the optimal L2 bound for the single scale Kakeya maximal function in the plane.

In this paper, we prove the sharp function inequality for the multilinear commutator related to the singular integral operator with variable Calderón-Zygmund kernel. By using the sharp inequality, we obtain the Lnorm inequality for the multilinear commutator. 2000 Mathematics Subject Classification: 42B20, 42B25.

We consider a collocation method for Cauchy singular integral equations on the interval based on weighted Chebyshev polynomials, where the coe cients of the operator are piecewise continuous. Stability conditions are derived using Banach algebra methods, and numerical results are given.

Abstract. Let (X, d, μ) be a metric measure space satisfying both the geometrically doubling and the upper doubling measure conditions, which is called nonhomogeneous metric measure space. In this paper, via a sharp maximal operator, the boundedness of commutators generated by multilinear singular integral with RBMO(μ) function on non-homogeneous metric measure spaces in m-multiple Lebesgue spa...

A well-known open problem of Muckenhoupt–Wheeden says that any Calderón–Zygmund singular integral operator T is of weak type (1,1) with respect to a couple of weights (w,Mw). In this paper, we consider a somewhat “dual” problem: sup λ>0 λw { x ∈Rn : |Tf (x)| Mw > λ } ≤ c ∫

Let T be a singular nonintegral operator; that is, it does not have an integral representation by a kernel with size estimates, even rough. In this paper, we consider the boundedness of commutators with T and Lipschitz functions. Applications include spectral multipliers of self-adjoint, positive operators, Riesz transforms of second-order divergence form operators, and fractional power of elli...