The main purpose of this paper is to prove Hörmander’s $L^p$–$L^q$ boundedness of Fourier multipliers on commutative hypergroups. We carry out this objective by establishing the Paley inequality and Hausdorff–Young–Paley inequality for commutative hypergroups. We show the $L^p$–$L^q$ boundedness of the spectral multipliers for the generalised radial Laplacian by examining our results on Chébli–Trimèche hypergroups. As a consequence, we obtain embedding theorems and time asymptotics for the $L^p$–$L^q$ norms of the heat kernel for generalised radial Laplacian.

This paper presents an analysis of unsteady flow of incompressible fractional Maxwell fluid filled in the annular region between two infinite coaxial circular cylinders. The fluid motion is created by the inner cylinder that applies a longitudinal time-dependent shear stress and the outer cylinder that is moving at a constant velocity. The velocity field and shear stress are determined using the Laplace and finite Hankel transforms. Obtained solutions are presented in terms of the generalized G and R functions. We also obtain the solutions for ordinary Maxwell fluid and Newtonian fluid as special cases of generalized solutions. The influence of different parameters on the velocity field and shear stress are also presented using graphical illustration. Finally, a comparison is drawn between motions of fractional Maxwell fluid, ordinary Maxwell fluid and Newtonian fluid.

This paper is concerned with an axially symmetric frictionless contact between an elastically transversely isptropic functionally graded half-space and a rigid base that has a small axisymmetric surface recess. The graded half-space is modeled as a nonhomogeneous medium. We reduce the problem to solving Fredholm integral equations, solve these equations numerically and establish a relationship between the applied pressure and gap radius. The effects of anisotropy and nonhomogeneity parameter of the graded half-space on the normal pressure as well as on the critical pressure have been shown graphically.

In this paper we establish that Hankel multipliers of Laplace transform type are bounded from ${{L}^{p}}\left( w \right)$ into itself when $1\,<\,p\,<\infty$, and from ${{L}^{1}}\left( w \right)$ into ${{L}^{1,\infty }}\left( w \right)$ , provided that $w$ is in the Muckenhoupt class ${{A}^{p}}$ on $\left( \left( 0,\,\infty \right),\,dx \right)$.

In this paper we study Hankel transforms and Hankel convolution operators on spaces of entire functions of finite order and their duals.

We derive an integral expression for the expected coverage of an n-dimensional target when the value density function of the target, the damage function, and the distribution of the damage function center around the target center are spherically symmetric. This integral expression is transformed by means of Parseval's theorem for Hankel transforms to an integral of the product of the Hankel transforms of order ½n − 1 of all underlying functions.