<i>L</i> <i>p</i> -<i>L</i> <i>q</i> Boundedness of <i>(k, a)</i>-Fourier Multipliers with Applications to Nonlinear Equations

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