Weak type estimates for Calderón‐Zygmund operators on Herz spaces at critical indexes

Abstract We define weak Herz spaces $ \dot K ^{\alpha , p, \infty} _{q} $(ℝn) which are the weak version of the ordinary Herz spaces $ \dot K ^{\alpha , p} _{q} $(ℝn). We consider the boundedness of Calderón‐Zygmund operators from $ \dot K ^{\alpha , p} _{q} $ to $ \dot K ^{\alpha , p, \infty} _{q} $ at critical indexes α = −n/q, n(1− 1/q) and q = 1. We also consider weighted estimates. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)