The Backward Shift on Dirichlet-type Spaces
نویسندگان
چکیده
We study the backward shift operator on Hilbert spaces Hα (for α ≥ 0) which are norm equivalent to the Dirichlet-type spaces Dα. Although these operators are unitarily equivalent to the adjoints of the forward shift operator on certain weighted Bergman spaces, our approach is direct and completely independent of the standard Cauchy duality. We employ only the classical Hardy space theory and an elementary formula expressing the inner product on Hα in terms of a weighted superposition of backward shifts.
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