Predual Spaces of Banach Completions of Orlicz-Hardy Spaces Associated with Operators

Let L be a linear operator in L(R) and generate an analytic semigroup {e}t≥0 with kernels satisfying an upper bound of Poisson type, whose decay is measured by θ(L) ∈ (0,∞]. Let ω on (0,∞) be of upper type 1 and of critical lower type p̃0(ω) ∈ (n/(n + θ(L)), 1] and ρ(t) = t/ω(t) for t ∈ (0,∞). In this paper, the authors first introduce the VMO-type space VMOρ,L(R ) and the tent space T ω,v(R n+1 + ) and characterize the space VMOρ,L(R ) via the space T ω,v(R n+1 + ). Let T̃ω(R n+1 + ) be the Banach completion of the tent space Tω(R n+1 + ). The authors then prove that T̃ω(R n+1 + ) is the dual space of T ω,v(R n+1 + ). As an application of this, the authors finally show that the dual space of VMOρ,L∗(R ) is the space Bω,L(R ), where L denotes the adjoint operator of L in L(R) and Bω,L(R ) the Banach completion of the Orlicz-Hardy space Hω,L(R ). These results generalize the known recent results by particularly taking ω(t) = t for t ∈ (0,∞).