On Lorentz spaces Γp,w


We study Lorentz spaces Γp,w where 0 < p < ∞, and w is a nonnegative measurable weight function. We first present some results concerning new formulas for the quasi-norm, duality, embeddings and Boyd indices. We then show that, whenever Γp,w does not coincide with L1 + L∞, it contains an order isomorphic and complemented copy of lp. We apply this result to determine criteria for order convexity and concavity as well as for lower and upper estimates. Finally, we characterize the type and cotype of Γp,w.

Publication Title

Israel Journal of Mathematics