Bounds on the Norm of the Backward Shift and Related Operators in Hardy and Bergman Spaces
Ferguson, Timothy
Original · EN
We study bounds for the backward shift operator f (f(z)-f(0))/z and the related operator f 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 M₁(r,u-u(0)) in terms of uₕ₁, where M₁ is the integral mean with p=1.
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