We characterize the weights w such that ∫0∞ f*(s)pw(s) ds ≃ ∫0∞ (f**(s) - f*(s))pw(s) ds. Our result generalizes a result due to Bennett-De Vore-Sharpley, where the usual Lorentz Lp,q norm is replaced by an equivalent expression involving the functional f** - f*. Sufficient conditions for the boundedness of maximal Calderón-Zygmund singular integral operators between classical Lorentz spaces are also given. © de Gruyter 2005.
|Publication status||Published - 1 Jan 2005|