Hardy's operator minus identity and power weights
arXiv:1909.04780 · doi:10.1016/j.jfa.2020.108532
Abstract
Let be the Hardy operator and the identity operator acting on functions on the real half-line. We find optimal bounds for the operator in the setting of power weights and the cases of positive decreasing functions, positive functions, and general functions. As a byproduct, we obtain some results about the optimal relations between the norms of and its dual.
22 pages