Bounds on the Norm of the Backward Shift and Related Operators in Hardy\n and Bergman Spaces

2017/02/10 by Timothy Ferguson, Ferguson, Timothy
Mathematics · #30H10 (Primary) 30H20 #47B36 #47B37 (Secondary) #Advanced Harmonic Analysis Research #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1702.03313

openalex publication_date 2017/02/10 · openalex created_date 2022/09/26 · openalex updated_date 2026/07/28

Abstract

We study bounds for the backward shift operator f \↦ (f(z)-f(0))/z and\nthe related operator f \↦ f - f(0) on Hardy and Bergman spaces of\nanalytic and harmonic functions. If u is a real valued harmonic function, we\nalso find a sharp bound on M₁(r,u-u(0)) in terms of \‖u\‖_h¹, where\nM₁ is the integral mean with p=1.\n

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