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 locala fractional maximal operators of orderαfrom L^(p)(v)to L^(q,∞)(u)with 1≤p≤q<∞under a condition of(u,v)∈∪b>a A_(p,q,a)^(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)∈M_(p,q,a)^(6a+9√da^2) and the two-weight strong-type boundedness of the local fractional integrals.These estimates are established by the radialization method and dyadic approach.

Real-Variable Theory of Local Variable Hardy Spaces

In this paper, we give a complete real-variable theory of local variable Hardy spaces.First, we present various real-variable characterization in terms of several local maximal functions.Next, the new atomic and the finite atomic decomposition for the local variable Hardy spaces are established. As an application, we also introduce the local variable Campanato space which is showed to be the dual space of the local variable Hardy spaces. Analogous to the homogeneous case, some equivalent definitions of the dual of local variable Hardy spaces are also considered. Finally, we show the boundedness of inhomogeneous Calderon–Zygmund singular integrals and local fractional integrals on local variable Hardy spaces and their duals.