Weighted (L, L) inequalities are studied for a variety of integral transforms of Fourier type. In particular, weighted norm inequalities for the Fourier, Hankel, and Jacobi transforms are derived from Calderón type rearrangement estimates. The obtained results keep their novelty even in the simplest cases of the studied transforms, the cosine and sine Fourier transforms. Sharpness of the condit...

In this paper we apply a method of spectral theory of linear operators [10] to establish relations between the support of a function f on R with properties of its image Tf under a linear operator T : R → R. The classical approach uses analytic continuation of the image Tf into some complex domain (theorems of Paley-Wiener type [4, 5, 6, 7]), and therefore, could not apply to functions whose ima...

It is well known that the Hankel transform possesses neither a shift-modulation nor a convolution-multiplication rule, both of which have found many uses when used with other integral transforms. In this paper, the generalized shift operator, as defined by Levitan, is applied to the Hankel transform. It is shown that under this generalized definition of shift, both convolution and shift theorem...

We deal with a class of one-parameter family integral transforms Bargmann type arising as dual transform fractional Hankel transform. Their ranges are identified to be special subspaces of...

A solution is presented to a doubly mixed boundary value problem of the torsion of an elastic layer, partially resting on a rigid circular base by a circular rigid punch attached to its surface. This problem is reduced to a system of dual integral equations using the Boussinesq stress functions and the Hankel integral transforms. With the help of the Gegenbauer expansion formula of the Bessel f...

We review the progress achieved in optical information processing during the last decade by applying fractional linear integral transforms. The fractional Fourier transform and its applications for phase retrieval, beam characterization, space-variant pattern recognition, adaptive filter design, encryption, watermarking, and so forth is discussed in detail. A general algorithm for the fractiona...

Correspondence: homidan@kfupm. edu.sa Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, P. O. Box 119, Saudi Arabia Abstract Hankel operators and Hankel transforms are required in a number of applications. This article proves a number of theorems that efficiently and accurately approximates a function using Hankel transforms and Hankel sum....

We extend to multilinear Hankel operators a result on the regularity of truncations of Hankel operators. We prove and use a continuity property on the bilinear Hilbert transforms on product of Lipschitz spaces and Hardy spaces. In this note, we want to extend to multilinear Hankel operators a result obtained by [BB] on the boundedness properties of truncation acting on bounded Hankel infinite m...