2024/12/31 by William L. Blair, Blair, William L. · 3 citations
Mathematics · #Algebraic and Geometric Analysis #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Spectral Theory in Mathematical Physics #math.AP #math.CA #math.CV #math.FA
paper · pdf · doi:10.48550/arxiv.2501.00542
published as Complex Variables and Elliptic Equations, 71(8) (2026) · Many typographical/notational errors corrected from the last version
openalex publication_date 2024/12/31 · arxiv created 2025/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28 · arxiv updated 2026/08/04
We develop representations for bicomplex-valued functions in Hardy classes that generalize the complex holomorphic Hardy spaces. Using these representations, we show these functions have boundary values in the sense of distributions that are representable by an atomic decomposition, and we show continuity of the Hilbert transform on this class of distributional boundary values.