Hardy Spaces (0

2017/08/27 by Guantie Deng, Rong Liu, Deng, Guantie +1
Mathematics · #30E25 #30H10 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Secondary: 30E20

paper · pdf · doi:10.48550/arxiv.1708.08762

openalex publication_date 2017/08/27 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

Let 00(∫_Γ |F(ζ+iτ)|^p | dζ|)^\frac1p< ∞. We denote the conformal mapping from ℂ₊ onto Ω₊ as Φ, and prove that, H^p(Ω₊) is isomorphic to H^p(ℂ₊), the classical Hardy space on the upper half plane~ℂ₊, under the mapping T\colon F→ F(Φ)⋅ (Φ')^\frac1p. Besides, T and T^-1 are both bounded. We also prove that if F(w)∈ H^p(Ω₊), then F(w) has non-tangential boundary limit F(ζ) a.e. on Γ, and, if 1\leqslant p< ∞, F(w) is the Cauchy integral on Γ of F(ζ).

Related

• Hardy Spaces (1
• Hardy's inequality and curvature
• Integral-type operators from Hardy space to Bloch space on the upper half-plane
• Boundary Hardy inequality on functions of bounded variation
• Hardy Spaces over Half-strip Domains