We study the boundedness and compactness of generalized Volterra integral operator on weighted Bergman spaces with doubling weights unit disc. A Toeplitz is defined boundedness, Schatten class membership this are investigated Hilbert space. As an application, operators also characterized. Finally, we get characterizations Hardy space $$H^2$$ .

Applying Baxter’s method of the Q-operator to the set of Sekiguchi’s commuting partial differential operators we show that Jack polynomials P (1/g) λ (x1, . . . , xn) are eigenfunctions of a one-parameter family of integral operators Qz. The operators Qz are expressed in terms of the Dirichlet-Liouville n-dimensional beta integral. From a composition of n operators Qzk we construct an integral ...

Applying Baxter’s method of the Q-operator to the set of Sekiguchi’s commuting partial differential operators we show that Jack’s symmetric polynomials P (1/g) λ (x1, . . . , xn) are eigenfunctions of a one-parameter family of integral operators Qz . The operators Qz are expressed in terms of the Dirichlet-Liouville n-dimensional beta integral. From a composition of n operators Qzk we construct...

For analytic functions in the open unit disk U , we define a new general integral operator. The main object of the this paper is to study this new integral operator and to determine univalence conditions of it. Several corollaries of the main results are also considered.

We analyze the spectrum of a certain singular integral operator on the space (L2(fi))3 where fi is contained in three dimensional Euclidean space and has a Lipschitz continuous boundary. This operator arises in the integral formulation of the magnetostatic field problem. We decompose (L2(fi))3 into invariant subspaces: in one where the operator is the zero map; in one, the identity map; and in ...

Let U = {z ∈ C : |z| < 1} be the unit disk in the complex plane, and let A be the class of functions which are analytic in the unit disk normalized with f (0) = f ′ (0)− 1 = 0. We denote by P the class of the functions p which are analytic in U , p (0) = 1 and Re p (z) > 0, for all z ∈ U . Let S be the subclass of A, consisting of all univalent functions f in U , and we consider S∗ the subclass...

In this paper we obtain the order of convexity for an integral operator in the classes B(μ, α),N(β), β − UCV(α) and β − Sp(α). 2000 Mathematics Subject Classification:30C45.

Due to rigorous work on integral operators and the hypergeomet-ric functions, we define here an integral operator involving generalized hypergeometric function. By means of this generalized function, we introduce new classes of analytic functions and study their properties. 1 Introduction and preliminaries. Let H be the class of functions analytic in U := {z ∈ C : |z| < 1} and A be the subclass...

Let 1 < p ≤ q < +∞ and let v, w be weights on (0,+∞) satisfying: (?) v(x)xis equivalent to a non-decreasing function on (0,+∞) for some ρ ≥ 0; [w(x)x] ≈ [v(x)x] for all x ∈ (0,+∞). We prove that if the averaging operator (Af)(x) := 1 x R x 0 f(t) dt, x ∈ (0,+∞), is bounded from the weighted Lebesgue space Lp((0,+∞); v) into the weighted Lebesgue space Lq((0,+∞);w), then there exists ε0 ∈ (0, p−...