2014/01/29 by Jun Cao, Cao, Jun, Der‐Chen Chang +5 · 1 citation
Mathematics · #42B30 #42B35 #46E30 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Primary: 47B06 #Secondary: 42B20
paper · pdf · doi:10.48550/arxiv.1401.7373
openalex publication_date 2014/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let φ be a Musielak-Orlicz function satisfying that, for any (x, t)∈ℝn×(0, ∞), φ(⋅, t) belongs to the Muckenhoupt weight class A_∞ (ℝn) with the critical weight exponent q(φ)∈[1, ∞) and φ(x, ⋅) is an Orlicz function with 0<i>(n-1)/(n), and via all the Riesz transforms with the order not more than m∈ℕ when (i(φ))/(q(φ))>(n-1)/(n+m-1). Moreover, the authors also establish the Riesz transform characterizations of Hφ(ℝn), respectively, by means of the higher order Riesz transforms defined via the homogenous harmonic polynomials or the odd order Riesz transforms. Even if when φ(x,t):=tw(x) for all x∈\mathbb Rn and t∈ [0,∞), these results also widen the range of weights in the known Riesz characterization of the classical weighted Hardy space H1w(\mathbb Rn) obtained by R. L. Wheeden from w∈ A1(\mathbb Rn) into w∈ A_∞(\mathbb Rn) with the sharp range q(w)∈ [1,\frac nn-1), where q(w) denotes the critical index of the weight w.</i>