On the kernels of Wiener-Hopf-Hankel operators on variable exponent Lebesgue spaces

Abstract

We investigate properties of the kernels (and cokernels) of Wiener-Hopf plus and minus Hankel operators on variable exponent Lebesgue spaces. Constructive operator identities are used in view to describe those kernels upon the consideration of auxiliary operators. Moreover, a Coburn-Simonenko type theorem is obtained for Wiener-Hopf plus and minus Hankel operators in the framework of variable exponent Lebesgue spaces.