In this paper, we establish the following limiting weak-type behaviors of Littlewood-Paley g-function g_φ: for nonnegative function f∈ L^1(R^n),■and ■where f_t(x) =t^(-n)f(t^(-1) x) for t > 0. Meanwhile, the co...In this paper, we establish the following limiting weak-type behaviors of Littlewood-Paley g-function g_φ: for nonnegative function f∈ L^1(R^n),■and ■where f_t(x) =t^(-n)f(t^(-1) x) for t > 0. Meanwhile, the corresponding results for Marcinkiewicz integral and its fractional version with kernels satisfying L_α~q-Dini condition are also given.展开更多
文摘In this paper, we establish the following limiting weak-type behaviors of Littlewood-Paley g-function g_φ: for nonnegative function f∈ L^1(R^n),■and ■where f_t(x) =t^(-n)f(t^(-1) x) for t > 0. Meanwhile, the corresponding results for Marcinkiewicz integral and its fractional version with kernels satisfying L_α~q-Dini condition are also given.
文摘为保证综合需求响应(integrated demand response,IDR)经济高效的实施,该文对传统用户模型提出3方面改进:首先考虑多种能源家用负荷使用时的耦合特性,建立能源舒适度耦合矩阵改进用户的舒适成本模型;进一步,引入参照依赖理论以描述不同时段激励间的耦合性,建立激励参照矩阵以优化用户响应量与激励价格的关联关系模型;最后,分析由于有限理性产生的羊群效应对用户参与IDR概率的影响,引入动态参与率以实现对用户间响应行为耦合特性的表征。在证明用户–多态能源服务商(multi-energy service provider,MESP)模型最优解唯一性的基础上,由仿真结果可知:考虑以上因素改进用户模型后,有效降低了响应偏差与MESP的总成本,提高了用户总收益与用能舒适度,实现了用户与MESP的共赢。研究表明,对于用户的精细化建模能够保障MESP以更低成本维持多态能源系统的供需平衡。
