Mean inequalities in certain Banach function spaces

Boundedness of the Hardy operator (Hf )(x) = x 0 f (t)dt and its adjoint (H∗f )(x) = ∞x f (t)dt is characterized between Banach function spaces Xq and Lp. By applying a limiting procedure, corresponding boundedness of the geometric mean operator (Gf )(x) = exp( 1 x x 0 lnf (t)dt) is also derived. © 2007 Elsevier Inc. All rights reserved