Boundedness of multidimensional hausdorff operators in h p spaces, 0 < p < 1

Sufficient conditions, of both smoothness and algebraic type, for the boundedness of multidimensional Hausdorff operators in Hardy spaces Hp(Rn), n ≥ 2, 0 < p < 1, are given. Positive and negative examples illustrate all aspects of the behavior of such operators and reveal the special nature of the case p < 1. © 2018 American Mathematical Society.