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The classical embedding theorem of Carleson deals with finite positive Borel measures µ on the closed unit disk for which there exists a positive constant c such that f L 2 (µ) ≤ cf H 2 for all f ∈ H 2 , the Hardy space of the unit disk. Lefèvre et al. examined measures µ for which there exists a positive constant c such that f L 2 (µ) ≥ cf H 2 for all f ∈… (More)

This paper concerns a family of weak parallelogram laws for Banach spaces. It is shown that the familiar Lebesgue spaces satisfy a range of these inequalities. Connections are made to basic geometric ideas, such as smoothness, convexity, and Pythagorean-type theorems. The results are applied to the linear prediction of random processes spanning a Banach… (More)

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