  The $(k,a)$-generalised Fourier transform is the unitary operator defined
using the $a$-deformed Dunkl harmonic oscillator.The main aim of this paper is
to prove $L^p$-$L^q$ boundedness of $(k, a)$-generalised Fourier multipliers.
To show the boundedness we first establish Paley inequality and
Hausdorff-Young-Paley inequality for $(k, a)$-generalised Fourier transform. We
also demonstrate applications of obtained results to study the well-posedness
of nonlinear partial differential equations.
