Weighted Composition Operators Acting on Harmonic Hardy Spaces

2017/08/17 by Pengyan Hu, Hu, Pengyan, Congwen Liu +5
Mathematics · #Advanced Harmonic Analysis Research #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Primary 47B33 #Secondary 31B05

paper · pdf · doi:10.48550/arxiv.1708.05225

openalex publication_date 2017/08/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Suppose n≥ 3 and let B be the open unit ball in ℝⁿ. Let φ: B→ B be a C² map whose Jacobian does not change sign, and let ψ be a C² function on B. We characterize bounded weighted composition operators W_φ,ψ acting on harmonic Hardy spaces h^p(B). In addition, we compute the operator norm of W_φ,ψ on h^p(B) when φ is a Möbius transformation of B.

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