2020/10/01 by Marijan Marković, Markovic, Marijan
Mathematics · #Advanced Harmonic Analysis Research #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.2010.00785
openalex publication_date 2020/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this note we obtain a version of the well-known Riesz's theorem on conjugate harmonic functions for Lumer's Hardy spaces (Lh)2(Ω) on arbitrary domains Ω: If a real-valued harmonic function U∈ (Lh)2(Ω) has a harmonic conjugate V on Ω (i.e., a real-valued harmonic function such that U+ iV is analytic on Ω), then U+iV also belongs to (Lh)2(Ω), and for the normalized conjugate we have the norm estimate ‖U+iV‖(Lh)2(Ω)≤√(2) ‖U‖(Lh)2(Ω), with the best possible constant.