Abstract
We study bounds for the backward shift operator $f\mapsto(f(z)-f(0))/z$ and the related operator $f\mapsto f-f(0)$ on Hardy and Bergman spaces of analytic and harmonic functions. If $u$ is a real valued harmonic function, we also find a sharp bound on $M_{1}(r,u-u(0))$ in terms of $\|u\|_{h^{1}}$, where $M_{1}$ is the integral mean with $p=1$.
Citation
Timothy Ferguson. "Bounds on the norm of the backward shift and related operators in Hardy and Bergman spaces." Illinois J. Math. 61 (1-2) 81 - 96, Spring and Summer 2017. https://doi.org/10.1215/ijm/1520046210
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