Characterizations of generalized Hardy and BMO spaces via square functions

Let d∈{3,4,5,…}. Consider L=−1 wdiv(A∇u)+μ over its maximal domain in Lw2(ℝ d). Under certain conditions on the weight w, the coefficient matrix A, and the positive Radon measure μ, we characterize the Hardy space H L1(ℝ d) and BMO space BMO L(ℝ d) associated with L using square functions. Other results include H L1(ℝ d)≡H L,max1(ℝ d) and (H L1(ℝ d))∗≡BMO L(ℝ d) as norm spaces, where H L,max1(ℝ d) denotes the maximal Hardy space associated with L.