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PROOF MINING IN Lp SPACES

Published online by Cambridge University Press:  29 August 2019

ANDREI SIPOŞ
ANDREI SIPOŞ*
Affiliation:
DEPARTMENT OF MATHEMATICS TECHNISCHE UNIVERSITÄT DARMSTADT SCHLOSSGARTENSTRASSE 7, 64289 DARMSTADT, GERMANY and SIMION STOILOW INSTITUTE OF MATHEMATICS OF THE ROMANIAN ACADEMY CALEA GRIVIŢEI 21, 010702BUCHAREST, ROMANIA E-mail: sipos@mathematik.tu-darmstadt.de Current address: DEPARTMENT OF MATHEMATICS TECHNISCHE UNIVERSITÄT DARMSTADT SCHLOSSGARTENSTRASSE 7, 64289DARMSTADT, GERMANY
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Abstract

We obtain an equivalent implicit characterization of Lp 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. As an aside, we obtain a concrete way of formalizing Lp spaces in positive-bounded logic. The axiomatization is followed by a corresponding metatheorem in the style of proof mining. We illustrate its use with the derivation for this class of spaces of the standard modulus of uniform convexity.

Keywords

03F1046B2546E30proof miningLp spacesuniform convexitymetatheorems
Type
Articles
Information
The Journal of Symbolic Logic , Volume 84 , Issue 4 , December 2019 , pp. 1612 - 1629
Copyright
Copyright © The Association for Symbolic Logic 2019 

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