Non-tangential Maximal Function Characterizations of Hardy Spaces Associated with Degenerate Elliptic Operators

Let w be either in the Muckenhoupt class of A(2)(R-n) weights or in the class of QC(R-n) weights, and let L-w := -w(-1) div(A del) be the degenerate elliptic operator on the Euclidean space R-n, n >= 2. In this article, the authors establish the non-tangential maximal function characterization of the Hardy space H-Lw(p) (R-n) associated with L-w for p epsilon (0, 1], and when p epsilon (n/n+1,1] and w epsilon A(q0) (R-n) with q(0) epsilon [1, p(n+1)/n), the authors prove that the associated Riesz transform del L-w(-1/2) is bounded from H-Lw(p) (R-n) to the weighted classical Hardy space H-w(p)(R-n).