The norm of a singular integral operator on an ellipse

The convexity of the integral operator on the class of the integral operator on the class B(mu,alpha)

In this paper, we study the convexity of the integral operator

Weighted norm inequalities for singular integral operators

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≡...

On an integral operator

In this paper we define a general integral operator for analytic functions in the open unit disk and we determine some conditions for univalence of this integral operator.

On The Perimeter of an Ellipse

Let E be the ellipse with major and minor radii a and b respectively, and Pbe its perimeter, then P = lim 4 tan(p/n)(a + b + 2) Σ a2 cos2 (2k-2)Pi/n+ sin2 (2k-2)Pi/n; where n = 2m. So without considering the limit, it gives a reasonable approxi-mation for P, it means that we can choose n large enough such that the amountof error be less than any given small number. On the other hand, the form...