$L^2$-oundedness of a singular integral operator

Self-adjointness of Cauchy Singular Integral Operator

We extend Krupnik’s criterion of self-adjointness of the Cauchy singular integral operator to the case of finitely connected domains. The main aim of the paper is to present a new approach for proof of the criterion. Let G+ be a finitely connected domain bounded by the rectifiable curve C = ∂G+, G− = C \ clos G+ and ∞ ∈ G−. Suppose also that w(z), z ∈ C is a nonnegative weight such that w(z) 6≡...

A Sharp Maximal Function Estimate for Vector-Valued Multilinear Singular Integral Operator

We establish a sharp maximal function estimate for some vector-valued multilinear singular integral operators. As an application, we obtain the $(L^p, L^q)$-norm inequality for vector-valued multilinear operators.

Some properties of a general integral operator

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 $mathcal{KD}(mu,beta).$‎

Numerical Solution of Singular IVPs of Lane-Emden Type Using Integral Operator and Radial Basis Functions

L2-boundedness of the Cauchy Integral Operator for Continuous Measures

1. Introduction. Let µ be a continuous (i.e., without atoms) positive Radon measure on the complex plane. The truncated Cauchy integral of a compactly supported function f in L p (µ), 1 ≤ p ≤ +∞, is defined by Ꮿ ε f (z) = |ξ −z|>ε f (ξ) ξ − z dµ(ξ), z ∈ C, ε > 0. In this paper, we consider the problem of describing in geometric terms those measures µ for which |Ꮿ ε f | 2 dµ ≤ C |f | 2 dµ, (1) f...