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Gesztesy, Fritz; Nichols, Roger; Stanfill, Jonathan
Complex analysis and operator theory, 03/2021, Letnik: 15, Številka: 2Journal Article
We survey some classical norm inequalities of Hardy, Kallman, Kato, Kolmogorov, Landau, Littlewood, and Rota of the type ‖ A f ‖ X 2 ≤ C ‖ f ‖ X ‖ A 2 f ‖ X , f ∈ dom ( A 2 ) , and recall that under exceedingly stronger hypotheses on the operator A and/or the Banach space X , the optimal constant C in these inequalities diminishes from 4 (e.g., when A is the generator of a C 0 contraction semigroup on a Banach space X ) all the way down to 1 (e.g., when A is a symmetric operator on a Hilbert space H ). We also survey some results in connection with an extension of the Hardy–Littlewood inequality involving quadratic forms as initiated by Everitt.
