TY - JOUR
AU - Jarno Talponen
PY - 2019/01/13
Y2 - 2019/09/21
TI - Duality of ODE-determined norms
JF - MATHEMATICA SCANDINAVICA
JA - MathScand
VL - 124
IS - 1
SE - Articles
DO - 10.7146/math.scand.a-109390
UR - https://www.mscand.dk/article/view/109390
AB - Recently the author initiated a novel approach to varying exponent Lebesgue space $L^{p(\cdot)}$ norms. In this approach the norm is defined by means of weak solutions to suitable first order ordinary differential equations (ODE). The resulting norm is equivalent with constant $2$ to a corresponding Nakano norm but the norms do not coincide in general and thus their isometric properties are different. In this paper the duality of these ODE-determined $L^{p(\cdot)}$ spaces is investigated. It turns out that the duality of the classical $L^p$ spaces generalizes nicely to this class of spaces. Here the duality pairing and HÃ¶lder's inequality work in the isometric sense which is a notable feature of these spaces. The uniform convexity and smoothness of these spaces are characterized under the anticipated conditions. A kind of universal space construction is also given for these spaces.
ER -