Rate of growth of hypercyclic and frequently hypercyclic functions for the Dunkl operator

For the Dunkl operator ${\mathrm{\Lambda }}_{\alpha }$ $(\alpha >-1\mathrm{/}2)$ on the space of entire functions on the complex space C, the critical rate of growth for the integral means $M_p(f,r)$ of their hypercyclic functions $f$ is obtained. The rate of growth of the corresponding frequently hypercyclic functions is also analyzed.