Monotonicity and rotundity of Lorentz spaces Γp,wΓp,w

Criteria for rotundity, strict monotonicity, and lower local uniform monotonicity of the Lorentz spaces Γp,wΓp,w of maximal functions are given under arbitrary nonnegative weight function ww. Necessary conditions are also established for uniform monotonicity of the spaces Γp,wΓp,w for 1≤p<∞1≤p<∞. Moreover, the spaces Γ1,wΓ1,w that are uniformly monotone are characterized.