Musielak-Orlicz Hardy spaces associated with divergence form elliptic operators without weight assumptions

Let L be a divergence form elliptic operator with complexbounded measurable coefficients, let ω be a positive Musielak-Orlicz functionon (0,∞) of uniformly strictly critical lower-type p _ω ε (0, 1], and let ρ(x, t) =t ^-1/ω-1(x, t ^-1) for x ε R ⁿ, t ε (0,∞). In this paper, we study the Musielak-Orlicz Hardy space Hω,L(R ⁿ) and its dual space BMOρ,L* (R ⁿ), where L*denotes the adjoint operator of L in L ²(R ⁿ). The ρ-Carleson measure characterizationand the John-Nirenberg inequality for the space BMOρ,L(R ⁿ) are also established. Finally, as applications, we show that the Riesz transform∇L- ^1/2 and the Littlewood-Paley g-function gL map H _ω,L(R ⁿ) continuouslyinto L(ω).