Two-weight Norm Inequalities for Local Fractional Integrals on Gaussian Measure Spaces

In this paper, the authors establish the two-weight boundedness of the local fractional maximal operators and local fractional integrals on Gaussian measure spaces associated with the local weights. More precisely, the authors first obtain the two-weight weak-type estimate for the local-a fractional maximal operators of order a from L-p(v) to L-q,L-infinity (u) with 1 <= p <= q < infinity under a condition of (u, v). is an element of boolean OR(b')(p,q,alpha), > A(p,q,alpha)(b') and then obtain the two-weight weak-type estimate for the local fractional integrals. In addition, the authors obtain the two-weight strong-type boundedness of the local fractional maximal operators under a condition of (u, v)is an element of M-p,q,alpha(6a+9 root da2) and the two-weight strong-type boundedness of the local fractional integrals. These estimates are established by the radialization method and dyadic approach.