Generalized area operators on L~p(R~n)

摘要

We introduce the generalized area operators by using nonnegative measures defined on upper half-spaces R_+~(n+1). The characterization of the boundedness and compactness of the generalized area operator from L~p(R~n) to L~q(R~n) is investigated in terms of s-Carleson measures with 1 ＜ p,q ＜ +∞. In the case of p = q = 1, the weak type estimate is also obtained.