Weighted Estimates for Generalised Conical Square Functions and Applications

Let{A_t}t>0 be a family of bounded linear operator on L2（X） where （X,d,μ） is a metric space with metric d and doubling measureμ.Assume that the family{A_t}t>0 satisfies suitable offdiagonal estimates from ■to L2for some p0<2.This paper aims to prove weighted bound estimates for conical square functions and g-functions associated to the family{A_t}t>0.Some applications such as weighted bounds for bilinear estimates associated to certain differential operators are also obtained.