Paley and Hardy's inequalities for the Fourier-Dunkl expansions

Purpose Paley's and Hardy's inequality are proved on a Hardy-type space for the Fourier–Dunkl expansions based complete orthonormal system of Dunkl kernels generalizing classical exponential defining Fourier series. Design/methodology/approach Although difficulties related to settings, techniques used by K. Sato were still efficient in this case establish inequalities which have expected similarities with case, Hardy Paley theorems Fourier–Bessel due fact that Bessel transform is even part transform. Findings expansions. Research limitations/implications This work participation extending harmonic analysis associated operators it shows utility BMO spaces some analytical results. Originality/value theory generalization special function root systems. Establishing these settings as has many applications mathematical physics framework vector valued extensions multipliers.