2017/07/19 by Jun Cao, Liguang Liu, Cao, Jun +5
Mathematics · #42B30 (Primary) #42B35 #46B70 (Secondary) #46E30 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.1707.05966
openalex publication_date 2017/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For any p∈(0, 1], let HΦp(ℝn) be the Musielak-Orlicz Hardy space associated with the Musielak-Orlicz growth function Φp, defined by setting, for any x∈ℝn and t∈[0, ∞), Φp(x, t):= \begincases \fractlog(e+t)+[t(1+|x|)n]1-p amp; when n(1/p-1)∉ ℕ ∪ \0\;
\fractlog(e+t)+[t(1+|x|)n]1-p[log(e+|x|)]p amp; when n(1/p-1)∈ ℕ∪\0\,
\endcases which is the sharp target space of the bilinear decomposition of the product of the Hardy space Hp(ℝn) and its dual. Moreover, HΦ1(ℝn) is the prototype appearing in the real-variable theory of general Musielak-Orlicz Hardy spaces. In this article, the authors find a new structure of the space HΦp(ℝn) by showing that, for any p∈(0, 1], HΦp(ℝn)=Hϕ0(ℝn) +HWpp(ℝn) and, for any p∈(0, 1), HΦp(ℝn)=H1(ℝn) +HWpp(ℝn), where H1(ℝn) denotes the classical real Hardy space, Hϕ0(ℝn) the Orlicz-Hardy space associated with the Orlicz function ϕ0(t):=t/log(e+t) for any t∈ [0,∞) and HWpp(ℝn) the weighted Hardy space associated with certain weight function Wp(x) that is comparable to Φp(x,1) for any x∈ℝn. As an application, the authors further establish an interpolation theorem of quasilinear operators based on this new structure.