Rate of growth of distributionally chaotic functions

We investigate the permissible growth rates of functions that are distributionally chaotic with respect to differentiation operators. improve on known estimates for $D$-distributionally entire functions, where is in terms average $L^p$-norms spheres radius $r>0$ as $r \to \infty$, $1 \leq p \infty$. compute $\partial/ \partial x_k$-distributionally harmonic $L^2$-norm also calculate sup-norm case partial operators $D^\alpha$.