This is an announcement for the paper “Proof mining in $L_p$ spaces” by Andrei Siposhttps://arxiv.org/find/math/1/au:+Sipos_A/0/1/0/all/0/1.

Abstract: We obtain an equivalent implicit characterization of $L_p$ Banach spaces that is amenable to a logical treatment. Using that, we obtain an axiomatization for such spaces into a higher-order logical system, the kind of which is used in proof mining, a research program that aims to obtain the hidden computational content of mathematical proofs using tools from mathematical logic. The axiomatization is followed by a corresponding metatheorem in the style of proof mining. We illustrate its use with an application, namely the derivation of the standard modulus of uniform convexity.

The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1609.02080