MSC 2010: 44A15, 44A20, 33C60Using the generalized confluent hypergeometric function [6] some new integral transforms are introduced. They are generalizations of some classical integral transforms, such as the Laplace, Stieltjes, Widder-potential, Glasser etc. integral transforms. The basic properties of these generalized integral transforms and their inversion formulas are obtained. Some examples are also given.
Let m: ℝ → ℝ be a function of bounded variation. We prove the -boundedness, 1 < p < ∞, of the one-dimensional integral operator defined by where for a family of functions satisfying conditions (1.1)-(1.3) given below.
The Stein-Weiss theorem that the distribution function of the Hilbert transform of the characteristic function of E depends only on the measure of E is generalized to the ergodic Hilbert transform.
Mathematics Subject Classification: 33C60, 33C20, 44A15This paper is devoted to an important case of Wright’s hypergeometric function 2Fτ,β1(a, b; c; z) = 2Fτ,β1(z), to studying its basic properties and to application of 2Fτ,β1(z) to the generalization of the associated Legendre functions.