In [3], Breaz and Breaz gave an univalence condition of the integral operator Gn,α introduced in [2]. The purpose of this paper is to give univalence condition of the generalized integral operator Gn,m,α defined in [4]. Our results generalize the results of [3]. 2000 Mathematics Subject Classification: 30C45.

If Ω is a ball in Rn (n ≥ 2), then the boundary integral operator of the double layer potential for the Laplacian is self-adjoint on L2(∂Ω). In this paper we prove that the ball is the only bounded Lipschitz domain on which the integral operator is self-adjoint.

We define a family of integral operators using multiplier transformation on the space of normalized meromorphic functions and introduce several new subclasses using this operator. We investigate various inclusion relations for these subclasses and some interesting applications involving a certain class of the integral operator are also considered.

We introduce an integral-type operator, denoted by P φ , on the space of holomorphic functions on the unit ball B ⊂ C, which is an extension of the product of composition and integral operators on the unit disk. The operator norm of P φ from the weighted Bergman space A p α B to the Bloch-type space Bμ B or the little Bloch-type space Bμ,0 B is calculated. The compactness of the operator is cha...

1 2 The paper deals with the basic integral equation of random field estimation theory by the criterion of minimum of variance of the error estimate. This integral equation is of the first kind. The corresponding integral operator over a bounded domain Ω in Rn is weakly singular. This operator is an isomorphism between appropriate Sobolev spaces. This is proved by a reduction of the integral eq...