This is an announcement for the paper "ODE representation for varying exponent $L^p$ norm" by Jarno Talponen.

Abstract: We will construct Banach function space norms arising as weak solutions to ordinary differential equations of first order. This provides as a special case a new way of defining varying exponent $L^p$ spaces, different from the Orlicz type approach. It turns out that the duality of these spaces behaves in an anticipated way, same as the uniform convexity and uniform smoothness.

Archive classification: math.FA math.CA

Mathematics Subject Classification: 46E30, 46B10, 34A12, 31B10

Submitted from: talponen@iki.fi

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1402.0528

or

http://arXiv.org/abs/1402.0528