Abstract
G. Bennett showed, by elementary proof, that if p≤q then (1.1) holds, and the constant p/s is best possible; and if p≥q then (1.2) is valid. The reversed inequalities have remained open problems. As a first step into the converse direction, what seems to be very intricate without additional assumptions, we prove the inverse inequalities under slight restrictions on the monotonicity of the parameters appearing in the problem.