Weighted Weak Local Hardy Spaces Associated with Schrödinger Operators

We characterize the weighted weak local hardy spaces wh ρp (ω) related to the critical radius function ρ and weights ω ∈ a ∞ ρ,∞ (rn) which locally behave as muckenhoupt's weights and actually include them,by the atomic decomposition. as an application,we show that localized riesz transforms are bounded on the weighted weak local hardy spaces. © 2015 hua zhu.