Monotonicity and rotundity of Lorentz spaces Γ p,w

Criteria for rotundity, strict monotonicity, and lower local uniform monotonicity of the Lorentz spaces Γ p,w of maximal functions are given under arbitrary nonnegative weight function w. Necessary conditions are also established for uniform monotonicity of the spaces Γ p,w for 1≤p\u3c∞. Moreover, the spaces Γ 1,w that are uniformly monotone are characterized. © 2011 Elsevier Ltd. All rights reserved