本刊英文版Vol.32(2016),No.11论文摘要（英文）

Sharp Bounds for Fractional One-sided Operators Maria Silvina RIVEROS Raul Emilio VIDAL Abstract In this paper,we characterize the sharp boundedness of the one-sided fractional maximal function for one-weight and two-weight inequalities.Also a new two-weight testing condition for the one-sided fractional maximal function is introduced extending the work of Martfn-Reyes and de la Torre.Improving.some extrapolation result for the one-sided case。

Abstract We develop a new method to perturb singular circuits in configuration space B with trivial isotropy groups, and construct a homomorphism Ф, between its circuit cobordism groups and pseudohomology groups. This work can be viewed as a counterpart to Zinger＇s construction.