Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 43, 2018, 737-754

DECOMPOSITIONS OF NAKANO NORMS BY ODE TECHNIQUES

Jarno Talponen

University of Eastern Finland, Department of Physics and Mathematics
Box 111, FI-80101 Joensuu, Finland; talponen 'at' iki.fi

Abstract. We study decompositions of Nakano type varying-exponent Lebesgue norms and spaces. These function spaces are represented here in a natural way as tractable varying-exponent l^p sums of projection bands. The main results involve embedding the variable Lebesgue spaces to such sums, as well as the corresponding isomorphism constants. The main tool applied here is an equivalent variable Lebesgue norm which is defined by a suitable ordinary differential equation introduced recently by the author. We also analyze the effect of transformations changing the ordering of the unit interval on the values of the ODE-determined norm.

2010 Mathematics Subject Classification: Primary 26D20, 46E30, 46E35.

Key words: Variable Lebesgue space, Musielak–Orlicz space, Nakano norm, ordinary differential equation, norm inequality, embedding theorem.

Reference to this article: J. Talponen: Decompositions of Nakano norms by ODE techniques. Ann. Acad. Sci. Fenn. Math. 43 (2018), 737-754.

Full document as PDF file

https://doi.org/10.5186/aasfm.2018.4346