2009/07/15 by Renjin Jiang, Dachun Yang, Jiang, Renjin +1
Mathematics · #42B30 #42B35 (Primary) #46E30 (Secondary) #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.0907.2605
openalex publication_date 2009/07/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let L be a divergence form elliptic operator with complex bounded measurable coefficients, ω a positive concave function on (0,∞) of strictly critical lower type pω∈ (0, 1] and ρ(t)=t-1/ω-1(t-1) for t∈ (0,∞). In this paper, the authors introduce the generalized VMO spaces \mathopVMO_ ρ, L(\mathbb Rn) associated with L, and characterize them via tent spaces. As applications, the authors show that (VMOρ,L (\mathbb Rn))^∗=Bω,L^∗(\mathbb Rn), where L^∗ denotes the adjoint operator of L in L2(\mathbb Rn) and Bω,L^∗(\mathbb Rn) the Banach completion of the Orlicz-Hardy space Hω,L^∗(\mathbb Rn). Notice that ω(t)=tp for all t∈ (0,∞) and p∈ (0,1] is a typical example of positive concave functions satisfying the assumptions. In particular, when p=1, then ρ(t)≡ 1 and (\mathopVMO1, L(\mathbb Rn))^∗=HL^∗1(\mathbb Rn), where HL^∗1(\mathbb Rn) was the Hardy space introduced by Hofmann and Mayboroda.