Inequalities for the gradient of eigenfunctions of the invariant laplacian in the unit ball

AbstractThe classical theorem of Hardy and Littlewood on differentiation in mixed normed spaces is discussed in the context of the class Xλ={f: f= λf}. The main result is that there is a difference between the cases λ = 0 and λ ≠ 0. In particular, if λ ≠ 0, then an Hp-norm is proportional to the corresponding Bloch type norm